{"id":23035,"date":"2023-01-30T09:54:20","date_gmt":"2023-01-30T09:54:20","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=23035"},"modified":"2023-02-20T08:48:01","modified_gmt":"2023-02-20T08:48:01","slug":"irregular-polygons","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/irregular-polygons","title":{"rendered":"Irregular Polygons"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-885778e0-cfbc-40c0-a132-c0288bc3a653\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/irregular-polygons#0-irregular-polygons-introduction>Irregular Polygons Introduction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/irregular-polygons#1-what-are-irregular-polygons>What Are Irregular Polygons?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/irregular-polygons#4-properties-of-irregular-polygons>Properties of Irregular Polygons<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/irregular-polygons#19-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/irregular-polygons#20-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/irregular-polygons#21-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"0-irregular-polygons-introduction\">Irregular Polygons Introduction<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">We know that a polygon is a two-dimensional enclosed figure made by joining three or more straight lines. A regular polygon is a type of a polygon that has equal sides and all interior angles of equal measure. If any one of the conditions is not met, it becomes an irregular polygon. Check out the irregular polygon shapes based on three conditions.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"554\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-2.png\" alt=\"Irregular polygons\" class=\"wp-image-23038\" title=\"Irregular polygons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-2-300x268.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Note that non-polygon shapes are the shapes that do not fulfill the criterion of a polygon. For example: Circle&nbsp;<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-missing-side-of-irregular-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_monsters_in_city_9_gm.png\" alt=\"Find Missing Side of Irregular Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Missing Side of Irregular Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-perimeter-of-irregular-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_monsters_in_city_6_gm.png\" alt=\"Find Perimeter of Irregular Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Perimeter of Irregular Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-perimeter-of-irregular-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_irregular_pt.png\" alt=\"Find the Perimeter of Irregular Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Perimeter of Irregular Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-perimeter-of-polygons\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_rectangle_1_pt.png\" alt=\"FInd the Perimeter of Polygons Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">FInd the Perimeter of Polygons Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-polygons-and-quadrilaterals\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_sort_shapes_broad_cat_pt.png\" alt=\"Identify Polygons and Quadrilaterals Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Polygons and Quadrilaterals Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-the-lines-of-symmetry-in-irregular-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_symm_irregular_shape_pt.png\" alt=\"Identify the LInes of Symmetry in Irregular Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify the LInes of Symmetry in Irregular Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"eplus-wrapper wp-block-heading\" id=\"1-what-are-irregular-polygons\">What Are Irregular Polygons?<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Irregular polygons <\/strong>are polygons that do not have equal sides and equal angles.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Common examples of irregular polygons are a scalene triangle, kite, rectangle.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">The image below shows the difference between a regular hexagon and an irregular hexagon.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"507\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-1.png\" alt=\"Regular polygon v. irregular polygon example\" class=\"wp-image-23037\" title=\"Regular polygon v. irregular polygon example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-1-300x245.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"2-irregular-polygons-definition\">Irregular Polygons: Definition<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">A polygon is said to be an irregular polygon or non-regular polygon if all the sides are not equal in length and and all the interior angles may not be of equal measure.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"3-how-to-classify-irregular-polygons\">How to Classify Irregular Polygons<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">We can classify irregular polygons based on the number of sides. A three-sided polygon is a triangle, a four-sided polygon is a quadrilateral, a five-sided polygon is a pentagon, and so on. Here are a few examples showing the names of irregular polygons and the number of sides:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"812\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-3.png\" alt=\"Irregular polygons\" class=\"wp-image-23039\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-3-229x300.png 229w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"4-properties-of-irregular-polygons\">Properties of Irregular Polygons<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">Let\u2019s see some properties of irregular polygons.<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">First, a regular polygon has equal sides and equal angles. If the polygon fails to meet one of these two conditions, it becomes an irregular polygon.<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Second, there are irregular polygons<strong> <\/strong>having equal sides but unequal angles and vice versa.<\/li>\n\n\n\n<li class=\" eplus-wrapper\">In the figure shown below, the shape is a rhombus. Is a rhombus a polygon? Yes, because it is a closed figure made of four line segments. A rhombus is an irregular polygon with equal sides and unequal angles.&nbsp;Its opposite angles are equal but all angles do not have the same measure.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"698\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-4.png\" alt=\"Rhombus as an irregular polygon\" class=\"wp-image-23040\" title=\"Rhombus as an irregular polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-4-266x300.png 266w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">In the above figure, shape B is a rectangle. Now, is a rectangle a polygon? Yes, it is, as it is a closed figure made of line segments. However, it is an irregular polygon with equal angles (90 degrees each) and unequal sides.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"5-common-types-of-irregular-polygons\">Common Types of Irregular Polygons<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">We will discuss some common irregular polygon examples along with their important properties.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"6-scalene-triangle-\"><strong>Scalene Triangle<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\">A scalene triangle has three unequal sides. So, it is an irregular polygon.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"369\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-5.png\" alt=\"Scalene triangle as an irregular polygon\" class=\"wp-image-23041\" title=\"Scalene triangle as an irregular polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-5-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">In the figure, the scalene triangle PQR is an <strong>irregular polygon <\/strong>as PQ, QR, and PR are of different lengths.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"7-isosceles-triangle-\"><strong>Isosceles Triangle<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\">An isosceles triangle has two equal sides $(\\text{AC} = \\text{AB})$ and two equal angles (angle C $=$ angle B). Since the third side and the third angle are not equal to the other two, it is an irregular polygon.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"636\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-6.png\" alt=\"isosceles triangle as an example of irregular polygon\" class=\"wp-image-23042\" title=\"isosceles triangle as an example of irregular polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-6.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-6-292x300.png 292w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"8-rectangle-\"><strong>Rectangle<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\">A rectangle ABCD has congruent angles (all angles are right angles), but it does not have equal sides. Since only the opposite sides are equal, a rectangle is an irregular polygon.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"503\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-7.png\" alt=\"Rectangle as an example of irregular polygon\" class=\"wp-image-23043\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-7.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-7-300x243.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"9-right-triangle-\"><strong>Right Triangle<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\">In the right triangle ABC, if the angle B is right angle, the angles A and B will be acute angles (the sum of all angles of a triangle is 180 degrees). Therefore, the three angles cannot be congruent. So, it is an irregular polygon. The following image shows an example of one such right triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"508\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-8.png\" alt=\"\" class=\"wp-image-23044\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-8.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-8-300x246.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"10-irregular-pentagon-\"><strong>Irregular Pentagon<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"420\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-9.png\" alt=\"Irregular pentagon\" class=\"wp-image-23045\" title=\"Irregular pentagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-9.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-9-300x203.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">An irregular pentagon is a polygon with five unequal sides. Since it does not have equal sides, it is an irregular polygon.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"11-irregular-hexagon-\"><strong>Irregular Hexagon<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"466\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-10.png\" alt=\"Irregular Hexagon\" class=\"wp-image-23046\" title=\"Irregular Hexagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-10.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-10-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">An irregular hexagon (or a non regular hexagon) has six unequal sides. So, a non-regular hexagon is an irregular polygon.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"12-formulas-associated-with-irregular-polygons\">Formulas Associated with Irregular Polygons<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">There are three formulas related to irregular polygons: area formula, perimeter formula, and angle-sum formula.&nbsp;<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"13-area-of-irregular-polygons-\"><strong>Area of Irregular Polygons<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\">Since irregular polygons come in different shapes and sizes, we do not have a standard formula for finding the area of an irregular polygon. So, we can divide it&nbsp;into regular polygons for which the area can be calculated and then we can add them to get the area of an irregular polygon.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">In the following figure, the irregular polygon can be divided into two triangles PQM and RSN, and a rectangle PQRS.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-11.png\" alt=\"Example of area of irregular polygons\" class=\"wp-image-23047\" title=\"Example of area of irregular polygons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-11.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-11-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">So, the area of the given irregular polygon $=$ Area of $\\angle$PQM $+$ Area of $\\angle$RSN $+$ Area of rectangle PQRS<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We can find the area of a triangle, provided that the base and height is known, by the formula:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Area of a triangle $= \\frac{1}{2}$ base $\\times$ height.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"14-perimeter-of-irregular-polygons-\"><strong>Perimeter of Irregular Polygons<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\">To find the perimeter of an irregular polygon, we have to add up the length of all its sides.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Consider the irregular polygon given below. The side lengths are a, b, c, d, e, f, g, h.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Perimeter $= a + b + c + d + e + f + g + h$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"572\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-12.png\" alt=\"Example of perimeter of an irregular polygon\" class=\"wp-image-23048\" title=\"Example of perimeter of an irregular polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-12.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-12-300x277.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"15-interior-angles-and-exterior-angles-\"><strong>Interior Angles and Exterior Angles<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\">When you extend a side of an irregular polygon, the angle formed between the extended side and its adjacent side is the exterior angle. On the other hand, interior angles are angles between a polygon&#8217;s two adjacent sides.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"578\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-13.png\" alt=\"Interior angles in an irregular pentagon\" class=\"wp-image-23049\" title=\"Interior angles in an irregular pentagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-13.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-13-300x280.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h4 class=\"eplus-wrapper wp-block-heading\" id=\"16-sum-of-interior-angles-of-irregular-polygons-\"><strong>Sum of Interior Angles of Irregular Polygons<\/strong><\/h4>\n\n\n\n<p class=\" eplus-wrapper\">The interior angle-sum formula for an <strong>irregular polygon <\/strong>is the same as the sum of interior angle in a regular polygon.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Sum of interior angles in a n-sided polygon $= (n \u2212 2) 180^{\\circ}$, where n is the number of sides of the irregular polygon.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example: What is the sum of the interior angles in a pentagon?<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Solution: A pentagon has 5 sides.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">So, $n = 5$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">The sum of interior angles of a regular polygon $= (5 \u2212 2) \\times 180^{\\circ}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= (5 \u2212 2) \\times 180^{\\circ}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 3 \\times 180$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;&nbsp; &nbsp; $= 540^{\\circ}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Therefore, the sum of interior angles of a pentagon is $540^{\\circ}$.<\/p>\n\n\n\n<h4 class=\"eplus-wrapper wp-block-heading\" id=\"17-sum-of-exterior-angles-of-irregular-polygons-\"><strong>Sum of Exterior Angles of Irregular Polygons<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"509\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-14.png\" alt=\"Interior angles and exterior angles in an irregular pentagon\" class=\"wp-image-23050\" title=\"Interior angles and exterior angles in an irregular pentagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-14.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-14-300x246.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">For any polygon, regular or non-regular, the sum of its exterior angles<strong>&nbsp;<\/strong>is 360 degrees.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"18-regular-polygons-vs-irregular-polygons-\"><strong>Regular Polygons vs. Irregular Polygons<\/strong><\/h2>\n\n\n\n<p class=\" eplus-wrapper\">Let&#8217;s now compare and contrast regular and irregular polygons.<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">All sides of a regular polygon are congruent.&nbsp;<\/li>\n<\/ol>\n\n\n\n<p class=\" eplus-wrapper\">Irregular polygons generally don&#8217;t have equal sides.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Rhombus is an example of an irregular polygon; it has equal sides, but unequal angles.<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Regular polygons have equal interior\/exterior angles.&nbsp;<\/li>\n<\/ol>\n\n\n\n<p class=\" eplus-wrapper\">In irregular polygons, the measure of all interior\/ exterior angles is not equal.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">A rectangle is an example of an irregular polygon where all the angles are equal but all sides are not of equal length.<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Regular polygons have equal sides and equal angles. Conversely, irregular polygons can either have equal sides or equal angles or none.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"762\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-15.png\" alt=\"Regular polygons and irregular polygons\" class=\"wp-image-23051\" title=\"Regular polygons and irregular polygons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-15.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/What-are-Irregular-Polygons-15-244x300.png 244w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"19-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>1. Find the perimeter of the below figure:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"320\" height=\"253\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-1-9.png\" alt=\"Finding perimeter of irregular polygon\" class=\"wp-image-23052\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-1-9.png 320w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-1-9-300x237.png 300w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">The perimeter of the irregular pentagon $ABCDE = AB + BC + CD + DE + AE$&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $= 12 + 10 + 6 + 4 + 7$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 39$ inches<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>2. Find the area of the below right triangle ABC.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"309\" height=\"173\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-2-7.png\" alt=\"Finding area of an irregular polygon\" class=\"wp-image-23053\" title=\"Finding area of an irregular polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-2-7.png 309w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Solved-Examples-2-7-300x168.png 300w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Area of the right triangle ABC $= \\frac{1}{2} \\times$ base $\\times$ height<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$= \\frac{1}{2} \\times$ BC $\\times$ AB<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$= \\frac{1}{2} \\times 6 \\times 3$&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$= 9$ $\\text{cm}^{2}$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>3.<\/strong> <strong>How many exterior angles are there in an irregular octagon?<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution: <\/strong>An irregular octagon has eight sides and eight interior angles. Therefore, it has eight exterior angles because the number of interior angles of a polygon is equal to its exterior angles.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>4. Find the sum of the interior angles of a polygon with eleven sides.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution: <\/strong>The sum of interior angles of an n-gon is $(n \u2212 2) \\times 180^{\\circ}$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Here, $n = 11$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">So, interior angle sum $= 9 \\times 180^{\\circ} = 1620^{\\circ}$ degrees.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>5. If the sum of the interior angles of an irregular polygon with \u201cn\u201d sides is 1800 degrees, what is n?<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution: <\/strong>Given the sum of the interior angles of an n-gon $= 1800^{\\circ}$&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(n \u2212 2) \u00d7 180^{\\circ} = 1800^{\\circ}$&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$n \u2212 2 = 10$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">So, $n = 12$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Therefore, the polygon has 12 sides.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"20-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Irregular Polygons<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The sum of interior angles of an irregular octagon is:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$540^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$720^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$900^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$1080^{\\circ}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $1080^{\\circ}$<br\/>Sum of interior angles of an irregular polygon $= (n - 2) \\times 180^{\\circ}$<br>\r\nAn octagon has 8 sides. So, $n = 8$<br>\r\n$(n - 2) \\times 180^{\\circ} = (8 - 2) \\times 180^{\\circ} = 6 \\times 180^{\\circ} = 1080^{\\circ}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The sum of exterior angles of an irregular triangle is:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$180^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$360^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$540^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$720^{\\circ}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $360^{\\circ}$<br\/>The sum of exterior angles of all polygons is $360^{\\circ}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The rhombus is irregular since it has<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">all sides unequal<\/div><div class=\"spq_answer_block\" data-value=\"1\">all angles equal<\/div><div class=\"spq_answer_block\" data-value=\"2\">only opposite sides equal<\/div><div class=\"spq_answer_block\" data-value=\"3\">all sides equal<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: all sides equal<br\/>All sides of a rhombus are equal. Its opposite angles are equal.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">A rectangle is irregular because:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">all its sides are equal<\/div><div class=\"spq_answer_block\" data-value=\"1\">all its angles are equal<\/div><div class=\"spq_answer_block\" data-value=\"2\">all its sides are not equal<\/div><div class=\"spq_answer_block\" data-value=\"3\">all its angles are not equal<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: all its sides are not equal<br\/>A rectangle is an irregular polygon. All angles of a rectangle are right angles, and thus congruent. However, all sides of a rectangle are not equal; only opposite sides are congruent.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Which of the following triangles is not an irregular polygon?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Scalene triangle<\/div><div class=\"spq_answer_block\" data-value=\"1\">Isosceles triangle<\/div><div class=\"spq_answer_block\" data-value=\"2\">Equilateral triangle<\/div><div class=\"spq_answer_block\" data-value=\"3\">Right triangle<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Equilateral triangle<br\/>Equilateral triangle has all sides congruent and all angles measure $60^{\\circ}$. So, it is a regular polygon.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Irregular Polygons\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Irregular Polygons\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The sum of interior angles of an irregular octagon is:\",\n                    \"text\": \"The sum of interior angles of an irregular octagon is:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Sum of interior angles of an irregular polygon $$= (n - 2) \\\\times 180^{\\\\circ}$$<br>\r\nAn octagon has 8 sides. So, $$n = 8$$<br>\r\n$$(n - 2) \\\\times 180^{\\\\circ} = (8 - 2) \\\\times 180^{\\\\circ} = 6 \\\\times 180^{\\\\circ} = 1080^{\\\\circ}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$540^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sum of interior angles of an irregular polygon $$= (n - 2) \\\\times 180^{\\\\circ}$$<br>\r\nAn octagon has 8 sides. So, $$n = 8$$<br>\r\n$$(n - 2) \\\\times 180^{\\\\circ} = (8 - 2) \\\\times 180^{\\\\circ} = 6 \\\\times 180^{\\\\circ} = 1080^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$720^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sum of interior angles of an irregular polygon $$= (n - 2) \\\\times 180^{\\\\circ}$$<br>\r\nAn octagon has 8 sides. So, $$n = 8$$<br>\r\n$$(n - 2) \\\\times 180^{\\\\circ} = (8 - 2) \\\\times 180^{\\\\circ} = 6 \\\\times 180^{\\\\circ} = 1080^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$900^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sum of interior angles of an irregular polygon $$= (n - 2) \\\\times 180^{\\\\circ}$$<br>\r\nAn octagon has 8 sides. So, $$n = 8$$<br>\r\n$$(n - 2) \\\\times 180^{\\\\circ} = (8 - 2) \\\\times 180^{\\\\circ} = 6 \\\\times 180^{\\\\circ} = 1080^{\\\\circ}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$1080^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Sum of interior angles of an irregular polygon $$= (n - 2) \\\\times 180^{\\\\circ}$$<br>\r\nAn octagon has 8 sides. So, $$n = 8$$<br>\r\n$$(n - 2) \\\\times 180^{\\\\circ} = (8 - 2) \\\\times 180^{\\\\circ} = 6 \\\\times 180^{\\\\circ} = 1080^{\\\\circ}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Sum of interior angles of an irregular polygon $$= (n - 2) \\\\times 180^{\\\\circ}$$<br>\r\nAn octagon has 8 sides. So, $$n = 8$$<br>\r\n$$(n - 2) \\\\times 180^{\\\\circ} = (8 - 2) \\\\times 180^{\\\\circ} = 6 \\\\times 180^{\\\\circ} = 1080^{\\\\circ}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The sum of exterior angles of an irregular triangle is:\",\n                    \"text\": \"The sum of exterior angles of an irregular triangle is:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The sum of exterior angles of all polygons is $$360^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$180^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of exterior angles of all polygons is $$360^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$540^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of exterior angles of all polygons is $$360^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$720^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of exterior angles of all polygons is $$360^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$360^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The sum of exterior angles of all polygons is $$360^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The sum of exterior angles of all polygons is $$360^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The rhombus is irregular since it has\",\n                    \"text\": \"The rhombus is irregular since it has\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"All sides of a rhombus are equal. Its opposite angles are equal.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"all sides unequal\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"All sides of a rhombus are equal. Its opposite angles are equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"all angles equal\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"All sides of a rhombus are equal. Its opposite angles are equal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"only opposite sides equal\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"All sides of a rhombus are equal. Its opposite angles are equal.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"all sides equal\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"All sides of a rhombus are equal. Its opposite angles are equal.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"All sides of a rhombus are equal. Its opposite angles are equal.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A rectangle is irregular because:\",\n                    \"text\": \"A rectangle is irregular because:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A rectangle is an irregular polygon. All angles of a rectangle are right angles, and thus congruent. However, all sides of a rectangle are not equal; only opposite sides are congruent.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"all its sides are equal\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A rectangle is an irregular polygon. All angles of a rectangle are right angles, and thus congruent. However, all sides of a rectangle are not equal; only opposite sides are congruent.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"all its angles are equal\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A rectangle is an irregular polygon. All angles of a rectangle are right angles, and thus congruent. However, all sides of a rectangle are not equal; only opposite sides are congruent.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"all its angles are not equal\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A rectangle is an irregular polygon. All angles of a rectangle are right angles, and thus congruent. However, all sides of a rectangle are not equal; only opposite sides are congruent.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"all its sides are not equal\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A rectangle is an irregular polygon. All angles of a rectangle are right angles, and thus congruent. However, all sides of a rectangle are not equal; only opposite sides are congruent.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A rectangle is an irregular polygon. All angles of a rectangle are right angles, and thus congruent. However, all sides of a rectangle are not equal; only opposite sides are congruent.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following triangles is not an irregular polygon?\",\n                    \"text\": \"Which of the following triangles is not an irregular polygon?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Equilateral triangle has all sides congruent and all angles measure $$60^{\\\\circ}$$. So, it is a regular polygon.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Scalene triangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Equilateral triangle has all sides congruent and all angles measure $$60^{\\\\circ}$$. So, it is a regular polygon.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Isosceles triangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Equilateral triangle has all sides congruent and all angles measure $$60^{\\\\circ}$$. So, it is a regular polygon.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Right triangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Equilateral triangle has all sides congruent and all angles measure $$60^{\\\\circ}$$. So, it is a regular polygon.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Equilateral triangle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Equilateral triangle has all sides congruent and all angles measure $$60^{\\\\circ}$$. So, it is a regular polygon.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Equilateral triangle has all sides congruent and all angles measure $$60^{\\\\circ}$$. So, it is a regular polygon.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"21-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-6a2642a9-2705-4c47-bb64-9979e14a1026\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-6a2642a9-2705-4c47-bb64-9979e14a1026\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6a2642a9-2705-4c47-bb64-9979e14a1026\"><strong>What are non-polygon shapes?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-6a2642a9-2705-4c47-bb64-9979e14a1026\">\n\n<p class=\" eplus-wrapper\">Non-polygon shapes are figures that do not satisfy the conditions of being polygon. Examples can be a circle and open shapes.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-6a2642a9-2705-4c47-bb64-9979e14a1026\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6a2642a9-2705-4c47-bb64-9979e14a1026\"><strong>How many triangles are required to form a polygon?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-6a2642a9-2705-4c47-bb64-9979e14a1026\">\n\n<p class=\" eplus-wrapper\">The number of triangles required to form a polygon is equal to the number of sides of a polygon minus two. If the polygon has \u201cn\u201d sides, then the number of triangles in a polygon is $(n \u2013 2)$.&nbsp;For examples, to form a rectangle (which has 4 sides), we need $4 &#8211; 2 = 2$ triangles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"538\" height=\"263\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-1-9.png\" alt=\"Numbers of triangles required to form a polygon\" class=\"wp-image-23055\" title=\"Numbers of triangles required to form a polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-1-9.png 538w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Practice-Problems-1-9-300x147.png 300w\" sizes=\"auto, (max-width: 538px) 100vw, 538px\" \/><\/figure>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-6a2642a9-2705-4c47-bb64-9979e14a1026\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6a2642a9-2705-4c47-bb64-9979e14a1026\"><strong>What is the difference between an equilateral irregular polygon and an equiangular irregular polygon?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-6a2642a9-2705-4c47-bb64-9979e14a1026\">\n\n<p class=\" eplus-wrapper\">Equilateral irregular polygons are irregular polygons that have equal sides but not equal angles. Conversely, equiangular irregular polygons are irregular polygons with equal angles but not equal sides.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-6a2642a9-2705-4c47-bb64-9979e14a1026\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6a2642a9-2705-4c47-bb64-9979e14a1026\"><strong>Is a parallelogram a regular polygon?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-6a2642a9-2705-4c47-bb64-9979e14a1026\">\n\n<p class=\" eplus-wrapper\">Parallelograms like rhombus and rectangles are irregular polygons, whereas a square, also a parallelogram, is a regular polygon.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-6a2642a9-2705-4c47-bb64-9979e14a1026\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6a2642a9-2705-4c47-bb64-9979e14a1026\"><strong>What is the sum of an irregular polygon&#8217;s interior and exterior angles at the same corner?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-6a2642a9-2705-4c47-bb64-9979e14a1026\">\n\n<p class=\" eplus-wrapper\">The interior angle and exterior angle of an irregular polygon at the same corner have a sum of 180 degrees (as it falls on a straight line).<\/p>\n\n<\/div><\/div>\n<\/div>\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"22-related-articles\">Related Articles<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\">Polygons<\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/regular-polygon\">Regular Polygons<\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/square\">Square<\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rectangle\">Rectangle<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Irregular Polygons Introduction We know that a polygon is a two-dimensional enclosed figure made by joining three or more straight lines. A regular polygon is a type of a polygon that has equal sides and all interior angles of equal measure. If any one of the conditions is not met, it becomes an irregular polygon. &#8230; <a title=\"Irregular Polygons\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/irregular-polygons\" aria-label=\"More on Irregular Polygons\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-23035","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23035","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=23035"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23035\/revisions"}],"predecessor-version":[{"id":25175,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23035\/revisions\/25175"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=23035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=23035"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=23035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}