{"id":35570,"date":"2023-11-08T16:30:00","date_gmt":"2023-11-08T16:30:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=35570"},"modified":"2023-11-09T05:27:54","modified_gmt":"2023-11-09T05:27:54","slug":"concave-polygon","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/concave-polygon","title":{"rendered":"Concave Polygon &#8211; Definition, Types, Properties, Examples, FAQs"},"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-bdae4dbe-d5bf-442d-bfe9-e211183f0ac8\" 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\/concave-polygon#0-what-are-concave-polygons>What Are Concave Polygons?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/concave-polygon#2-properties-of-concave-polygon>Properties of Concave Polygon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/concave-polygon#3-concave-polygon-vs-convex-polygon>Concave Polygon vs. Convex Polygon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/concave-polygon#7-solved-examples-on-concave-polygons>Solved Examples on Concave Polygons<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/concave-polygon#8-practice-problems-on-concave-polygons>Practice Problems on Concave Polygons<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/concave-polygon#9-frequently-asked-questions-about-concave-polygons>Frequently Asked Questions about Concave Polygons<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-concave-polygons\">What Are Concave Polygons?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>A concave polygon is a <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\"><strong>polygon<\/strong><\/a><strong> in which at least one interior angle is a reflex angle (angle greater than 180\u00b0 but less than 360\u00b0).&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A concave polygon has at least 4 sides. It means that a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangle<\/a> is always a convex polygon. The diagonals in a concave polygon may lie partly or fully outside the polygon.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles\">interior angles<\/a> are not equal, all concave polygons are \u201c<a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/irregular-polygons\">irregular polygons<\/a>.\u201d If you connect any two points inside or on the polygon by a straight line, and it goes outside the polygon, then the polygon is concave.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"617\" height=\"360\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/concave-polygon-interior-angles-and-diagonal-properties.png\" alt=\"Concave polygon - interior angles and diagonal properties\" class=\"wp-image-35576\" title=\"Concave polygon - interior angles and diagonal properties\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/concave-polygon-interior-angles-and-diagonal-properties.png 617w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/concave-polygon-interior-angles-and-diagonal-properties-300x175.png 300w\" sizes=\"auto, (max-width: 617px) 100vw, 617px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/geometry\">geometry<\/a>, a polygon can be defined as a flat or plane, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/2-dimensional\">two-dimensional<\/a> <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/closed-shape\">closed shape<\/a>, bounded with straight sides. It does not have <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/curve\">curved<\/a> edges. There are two types of polygons based on the measure of interior angles.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/convex-polygon\">Convex Polygons<\/a>&nbsp;<\/li>\n\n\n\n<li>Concave Polygons<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The term \u201cconcave\u201d refers to a shape having an outline or surface that curves inwards. Concave polygons have dents. Take a look at a few examples of concave polygons.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"560\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/examples-of-concave-polygons.png\" alt=\"Examples of concave polygons\" class=\"wp-image-35578\" title=\"Examples of concave polygons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/examples-of-concave-polygons.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/examples-of-concave-polygons-300x271.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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-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><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=\"wp-block-heading\" id=\"1-concave-polygon-definition\">Concave Polygon: Definition<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If the measure of at least one interior angle of a polygon is greater than 180 degrees, the polygon is said to be a concave polygon.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-properties-of-concave-polygon\">Properties of Concave Polygon<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>There is at least one angle in a concave polygon which is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/reflex-angle\">reflex angle<\/a> (greater than 180\u00b0 and less than 360\u00b0).<\/li>\n\n\n\n<li>One or more diagonals in a concave polygon are partly or fully outside.<\/li>\n\n\n\n<li>There is at least one <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/vertex\">vertex<\/a> in a concave polygon that seems to be pushed inwards to give that distinct \u201ccave\u201d shape or dented shape to the polygon.<\/li>\n\n\n\n<li>If we draw a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/line-segment\">line segment<\/a> across a concave polygon, it touches more than 2 sides.&nbsp;<\/li>\n\n\n\n<li>Concave polygons are irregular polygons.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"406\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/properties-of-a-concave-polygon.png\" alt=\"Properties of a concave polygon\" class=\"wp-image-35579\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/properties-of-a-concave-polygon.png 619w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/properties-of-a-concave-polygon-300x197.png 300w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-concave-polygon-vs-convex-polygon\">Concave Polygon vs. Convex Polygon<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Convex Polygons<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Concave Polygons<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">All interior angles are less than 180\u00b0.<\/td><td class=\"has-text-align-left\" data-align=\"left\">It has at least one interior angle greater than 180\u00b0 (reflex).<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">The minimum number of sides of a convex polygon is 3.<\/td><td class=\"has-text-align-left\" data-align=\"left\">The minimum number of sides of a concave polygon is 4.<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">When we draw a line inside a convex shape from any one side, it touches only 2 sides.<\/td><td class=\"has-text-align-left\" data-align=\"left\">When we draw a line inside a concave shape from one side, it touches more than 2 sides.<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">The diagonals in a convex polygon do not lie outside the polygon.<\/td><td class=\"has-text-align-left\" data-align=\"left\">One or more diagonals in a concave polygon are partly or fully outside it.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-angles-in-a-concave-polygon\">Angles in a Concave Polygon<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s discuss formulas for the sum of interior angles and the sum of exterior angles in a concave polygon.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sum of Exterior Angles of a Concave Polygon<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Like any other polygon, the sum of the exterior angles of a concave polygon is 360\u00b0. This means the exterior angles always add up to 360\u00b0 for all concave polygons.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sum of Interior Angles of a Concave Polygon<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">To find the sum of interior angles of a concave polygon, we use the same formula that is applied for any other polygon.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sum of interior angles = (n &#8211; 2) \u00d7 180\u00b0, where \u201cn\u201d is the number of sides of a polygon.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-concave-polygon-formulas\">Concave Polygon Formulas<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s understand how to find the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/area-and-perimeter\">area and perimeter<\/a> of a concave polygon.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Perimeter of a Concave Polygon<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Perimeter of a concave polygon is simply the total length of its outer boundary. To find the perimeter of a concave polygon, simply add the length of all its sides.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> The perimeter of the given polygon is 4 + 4 + 4 + 4 + 8 = 24 units<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"617\" height=\"402\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/perimeter-of-a-concave-polygon.png\" alt=\"Perimeter of a concave polygon\" class=\"wp-image-35580\" title=\"Perimeter of a concave polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/perimeter-of-a-concave-polygon.png 617w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/perimeter-of-a-concave-polygon-300x195.png 300w\" sizes=\"auto, (max-width: 617px) 100vw, 617px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Area of a Concave Polygon<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Concave polygons are irregular polygons. Thus, to find the area of a concave polygon, we simply break it into the shapes whose <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/area\">area<\/a> can be calculated with a formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> The area of the given polygon is simply the sum of the area of the four triangles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"420\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/area-of-a-concave-polygon.png\" alt=\"Area of a concave polygon\" class=\"wp-image-35581\" title=\"Area of a concave polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/area-of-a-concave-polygon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/area-of-a-concave-polygon-300x203.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-concave-polygons-in-real-life\">Concave Polygons in Real Life<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Concave polygons have a peculiar shape in which at least one of the vertices is pointed inwards. We can notice concave polygons in our day-to-day life. Let\u2019s take a look at convex and concave shapes around us.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Concave polygon shapes:<\/strong><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"356\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/examples-of-concave-polygons-in-real-life.png\" alt=\"Examples of concave polygons in real life\" class=\"wp-image-35582\" title=\"Examples of concave polygons in real life\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/examples-of-concave-polygons-in-real-life.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/examples-of-concave-polygons-in-real-life-300x172.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-solved-examples-on-concave-polygons\">Solved Examples on Concave Polygons<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. If the number of sides of a concave polygon is 5, then what will be the sum of its interior angles?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of sides = n = 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sum of interior angles = (n &#8211; 2) \u00d7 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;=(5 &#8211; 2) \u00d7 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;=3 \u00d7 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a0 = 540\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Which of the following are concave polygons?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"519\" height=\"100\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/example-on-identifying-concave-polygons.png\" alt=\"Example on identifying concave polygons\" class=\"wp-image-35583\" title=\"Example on identifying concave polygons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/example-on-identifying-concave-polygons.png 519w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/example-on-identifying-concave-polygons-300x58.png 300w\" sizes=\"auto, (max-width: 519px) 100vw, 519px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Concave polygons have a dent or a vertex turned inwards. At least one interior angle measures greater than 180 degrees.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Concave Polygons: B, E, F<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Convex Polygons: A, C, D<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Find the value of the interior angle \u2220E.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"301\" height=\"281\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/angles-in-a-concave-polygon-example.png\" alt=\"Angles in a concave polygon - example\" class=\"wp-image-35584\" title=\"Angles in a concave polygon - example\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">n=6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sum of interior angles\u00a0 = (n-2) \u00d7 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a0\u00a0\u00a0\u00a0= (6-2) \u00d7 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a0\u00a0\u00a0\u00a0= 4 \u00d7 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a0\u00a0\u00a0\u00a0= 720\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In hexagon ABCDEF,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">m\u2220A + m\u2220B + m\u2220C + m\u2220D + m\u2220E + m\u2220F = 720\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">m\u2220E + 49\u00b0 + 120\u00b0 + 120\u00b0 + 120\u00b0 + 76\u00b0 = 720\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">m\u2220E + 485\u00b0 = 720\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">m\u2220E = 720\u00b0-485\u00b0&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">m\u2220E =235\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. Find the perimeter of the given convex polygon.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"311\" height=\"374\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/arrow-concave-polygon.png\" alt=\"Arrow - concave polygon\" class=\"wp-image-35586\" title=\"Arrow - concave polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/arrow-concave-polygon.png 311w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/arrow-concave-polygon-249x300.png 249w\" sizes=\"auto, (max-width: 311px) 100vw, 311px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Perimeter is the total length of the outer boundary.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, perimeter of the given polygon = (a + b + c + d) units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>5.<\/strong><strong> Fill in the blanks with the correct word.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>(a) In a _____ polygon, at least one angle is greater than <\/strong><strong>180\u00b0<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>(b) A polygon with all interior angles less than <\/strong><strong>180\u00b0<\/strong><strong> is a ____ polygon.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>(c) The sum of the exterior angles of a concave polygon is _____.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(a) In a concave polygon, at least one angle is greater than <strong>180\u00b0<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(b) A polygon with all interior angles less than 180\u00b0 is a convex polygon.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(c) The sum of the exterior angles of a concave polygon is 360<sup>o<\/sup>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-practice-problems-on-concave-polygons\">Practice Problems on Concave Polygons<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Concave Polygon - Definition, Types, Properties, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following is NOT a concave polygon?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/Identifying-concave-polygons.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">Image A<\/div><div class=\"spq_answer_block\" data-value=\"1\">Image B<\/div><div class=\"spq_answer_block\" data-value=\"2\">Image C<\/div><div class=\"spq_answer_block\" data-value=\"3\">Image D<\/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: Image B<br\/>A triangle is always a convex polygon. The sum of angles in a triangle is 180 degrees. So, a triangle can never be a concave polygon.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following is a property of a concave polygon?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">All the diagonals lie inside the polygon.<\/div><div class=\"spq_answer_block\" data-value=\"1\">All the angles in the polygon are acute angles.<\/div><div class=\"spq_answer_block\" data-value=\"2\">The sum of interior angles of a concave polygon is 360\u00b0.<\/div><div class=\"spq_answer_block\" data-value=\"3\">At least one angle in the polygon is greater than 180\u00b0.<\/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: At least one angle in the polygon is greater than 180\u00b0.<br\/>A, B and C are not the properties of a concave polygon. One or more diagonals lie outside the polygon. The sum of interior angles of a concave polygon is $(n \\;-\\; 2) \\times 180^{\\circ}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The minimum number of sides of a concave polygon is _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2<\/div><div class=\"spq_answer_block\" data-value=\"1\">3<\/div><div class=\"spq_answer_block\" data-value=\"2\">4<\/div><div class=\"spq_answer_block\" data-value=\"3\">5<\/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: 4<br\/>The minimum number of sides of a concave polygon is 4.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of the following shapes represent a concave polygon?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Star<\/div><div class=\"spq_answer_block\" data-value=\"1\">Parallelogram<\/div><div class=\"spq_answer_block\" data-value=\"2\">Square<\/div><div class=\"spq_answer_block\" data-value=\"3\">Regular Pentagon<\/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: Star<br\/>A star is a concave shape.<\/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\">One or more diagonals of a concave polygon lie _______ the polygon.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">inside<\/div><div class=\"spq_answer_block\" data-value=\"1\">on the boundary of<\/div><div class=\"spq_answer_block\" data-value=\"2\">outside<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: outside<br\/>Some diagonals of a concave polygon lie outside the polygon.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">6<\/span><h3 class=\"sqp_question_text\">Regular polygons can never be _____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">convex<\/div><div class=\"spq_answer_block\" data-value=\"1\">concave<\/div><div class=\"spq_answer_block\" data-value=\"2\">Simple<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/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: concave<br\/>Regular polygons can never be concave. All the concave polygons are irregular polygons.<\/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\": \"Concave Polygon - Definition, Types, Properties, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Concave Polygon\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is NOT a concave polygon?\",\n                    \"text\": \"Which of the following is NOT a concave polygon? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/Identifying-concave-polygons.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A triangle is always a convex polygon. The sum of angles in a triangle is 180 degrees. So, a triangle can never be a concave polygon.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Image A\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangle is always a convex polygon. The sum of angles in a triangle is 180 degrees. So, a triangle can never be a concave polygon.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Image C\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangle is always a convex polygon. The sum of angles in a triangle is 180 degrees. So, a triangle can never be a concave polygon.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Image D\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangle is always a convex polygon. The sum of angles in a triangle is 180 degrees. So, a triangle can never be a concave polygon.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Image B\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A triangle is always a convex polygon. The sum of angles in a triangle is 180 degrees. So, a triangle can never be a concave polygon.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A triangle is always a convex polygon. The sum of angles in a triangle is 180 degrees. So, a triangle can never be a concave polygon.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is a property of a concave polygon?\",\n                    \"text\": \"Which of the following is a property of a concave polygon?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A, B and C are not the properties of a concave polygon. One or more diagonals lie outside the polygon. The sum of interior angles of a concave polygon is $$(n \\\\;-\\\\; 2) \\\\times 180^{\\\\circ}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"All the diagonals lie inside the polygon.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A, B and C are not the properties of a concave polygon. One or more diagonals lie outside the polygon. The sum of interior angles of a concave polygon is $$(n \\\\;-\\\\; 2) \\\\times 180^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"All the angles in the polygon are acute angles.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A, B and C are not the properties of a concave polygon. One or more diagonals lie outside the polygon. The sum of interior angles of a concave polygon is $$(n \\\\;-\\\\; 2) \\\\times 180^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The sum of interior angles of a concave polygon is 360\u00b0.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A, B and C are not the properties of a concave polygon. One or more diagonals lie outside the polygon. The sum of interior angles of a concave polygon is $$(n \\\\;-\\\\; 2) \\\\times 180^{\\\\circ}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"At least one angle in the polygon is greater than 180\u00b0.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A, B and C are not the properties of a concave polygon. One or more diagonals lie outside the polygon. The sum of interior angles of a concave polygon is $$(n \\\\;-\\\\; 2) \\\\times 180^{\\\\circ}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A, B and C are not the properties of a concave polygon. One or more diagonals lie outside the polygon. The sum of interior angles of a concave polygon is $$(n \\\\;-\\\\; 2) \\\\times 180^{\\\\circ}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The minimum number of sides of a concave polygon is _______.\",\n                    \"text\": \"The minimum number of sides of a concave polygon is _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The minimum number of sides of a concave polygon is 4.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The minimum number of sides of a concave polygon is 4.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The minimum number of sides of a concave polygon is 4.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The minimum number of sides of a concave polygon is 4.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"4\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The minimum number of sides of a concave polygon is 4.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The minimum number of sides of a concave polygon is 4.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following shapes represent a concave polygon?\",\n                    \"text\": \"Which of the following shapes represent a concave polygon?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A star is a concave shape.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Parallelogram\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A star is a concave shape.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Square\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A star is a concave shape.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Regular Pentagon\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A star is a concave shape.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Star\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A star is a concave shape.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A star is a concave shape.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"One or more diagonals of a concave polygon lie _______ the polygon.\",\n                    \"text\": \"One or more diagonals of a concave polygon lie _______ the polygon.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Some diagonals of a concave polygon lie outside the polygon.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"inside\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Some diagonals of a concave polygon lie outside the polygon.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"on the boundary of\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Some diagonals of a concave polygon lie outside the polygon.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Some diagonals of a concave polygon lie outside the polygon.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"outside\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Some diagonals of a concave polygon lie outside the polygon.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Some diagonals of a concave polygon lie outside the polygon.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Regular polygons can never be _____.\",\n                    \"text\": \"Regular polygons can never be _____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Regular polygons can never be concave. All the concave polygons are irregular polygons.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"convex\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Regular polygons can never be concave. All the concave polygons are irregular polygons.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Simple\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Regular polygons can never be concave. All the concave polygons are irregular polygons.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Regular polygons can never be concave. All the concave polygons are irregular polygons.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"concave\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Regular polygons can never be concave. All the concave polygons are irregular polygons.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Regular polygons can never be concave. All the concave polygons are irregular polygons.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-frequently-asked-questions-about-concave-polygons\">Frequently Asked Questions about Concave Polygons<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-fc3affa4-29d4-4777-8aae-89c2480fa179\" 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-fc3affa4-29d4-4777-8aae-89c2480fa179\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-fc3affa4-29d4-4777-8aae-89c2480fa179\"><strong>How can we find the perimeter of a concave 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-0-fc3affa4-29d4-4777-8aae-89c2480fa179\">\n\n<p class=\"wp-block-paragraph\">The perimeter of a concave polygon is calculated in the same way as the perimeter of convex polygons. All the sides of the polygon are added to find the perimeter.<\/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-fc3affa4-29d4-4777-8aae-89c2480fa179\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-fc3affa4-29d4-4777-8aae-89c2480fa179\"><strong>How can we find the area of a concave 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-fc3affa4-29d4-4777-8aae-89c2480fa179\">\n\n<p class=\"wp-block-paragraph\">Concave polygons are irregular in shape. A concave polygon can be divided into triangles or other smaller polygons. Then, the area of these shapes can be calculated with the appropriate formulas and these areas can be added together to get the area of the concave 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-2-fc3affa4-29d4-4777-8aae-89c2480fa179\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-fc3affa4-29d4-4777-8aae-89c2480fa179\"><strong>Why is an arrow a concave 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-fc3affa4-29d4-4777-8aae-89c2480fa179\">\n\n<p class=\"wp-block-paragraph\">An arrow is a concave polygon because it fulfills all the conditions of a concave polygon. It has interior angles that measure more than 180\u00b0 and one diagonal in an arrow lies outside the shape.<\/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-fc3affa4-29d4-4777-8aae-89c2480fa179\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-fc3affa4-29d4-4777-8aae-89c2480fa179\"><strong>What is the difference between a regular polygon and a concave 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-fc3affa4-29d4-4777-8aae-89c2480fa179\">\n\n<p class=\"wp-block-paragraph\">A regular polygon is a polygon that is equilateral and equiangular whereas a concave polygon is a polygon in which at least one angle is more than 180\u00b0.<\/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-fc3affa4-29d4-4777-8aae-89c2480fa179\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-fc3affa4-29d4-4777-8aae-89c2480fa179\"><strong>Is a triangle a concave 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-4-fc3affa4-29d4-4777-8aae-89c2480fa179\">\n\n<p class=\"wp-block-paragraph\">No, a triangle is not a concave polygon as there are no diagonals in a triangle. Also, the sum of angles of a triangle is 180\u00b0.<\/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-5-fc3affa4-29d4-4777-8aae-89c2480fa179\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-fc3affa4-29d4-4777-8aae-89c2480fa179\"><strong>Is a star a concave 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-5-fc3affa4-29d4-4777-8aae-89c2480fa179\">\n\n<p class=\"wp-block-paragraph\">A star is a concave polygon.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Concave Polygons? A concave polygon is a polygon in which at least one interior angle is a reflex angle (angle greater than 180\u00b0 but less than 360\u00b0).&nbsp; A concave polygon has at least 4 sides. It means that a triangle is always a convex polygon. The diagonals in a concave polygon may lie &#8230; <a title=\"Concave Polygon &#8211; Definition, Types, Properties, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/concave-polygon\" aria-label=\"More on Concave Polygon &#8211; Definition, Types, Properties, Examples, FAQs\">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-35570","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\/35570","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=35570"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35570\/revisions"}],"predecessor-version":[{"id":35593,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35570\/revisions\/35593"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=35570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=35570"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=35570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}