{"id":28282,"date":"2023-04-27T16:50:09","date_gmt":"2023-04-27T16:50:09","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=28282"},"modified":"2023-10-04T05:15:01","modified_gmt":"2023-10-04T05:15:01","slug":"convex-polygon-definition-formula-properties-types-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/convex-polygon","title":{"rendered":"Convex Polygon &#8211; Definition, Formula, Properties, Types, Examples"},"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-918406f4-4c5e-40de-9da5-d5883a4da5a8\" 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\/convex-polygon#0-what-is-a-convex-polygon>What Is a Convex Polygon?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/convex-polygon#3-types-of-convex-polygons>Types of Convex Polygons<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/convex-polygon#13-difference-between-concave-polygon-and-convex-polygon>Difference between Concave Polygon and Convex Polygon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/convex-polygon#15-solved-examples-on-convex-polygon>Solved Examples on Convex Polygon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/convex-polygon#16-practice-problems-on-convex-polygon>Practice Problems on Convex Polygon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/convex-polygon#17-frequently-asked-questions-on-convex-polygons>Frequently Asked Questions on Convex Polygons<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-convex-polygon\">What Is a Convex Polygon?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>A convex polygon is a polygon with all interior angles less than <\/strong>$180^\\circ$<strong> and vertices are pointed outwards.<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In convex polygons, all diagonals are in the interior of the polygon. All the vertices of a complex polygon point outwards. A regular polygon in geometry is always convex. Any closed shape that has a curved surface is convex. Take a look at the image given below to understand it better.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"391\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/examples-of-convex-polygons.png\" alt=\"Examples of convex polygons\" class=\"wp-image-34557\" title=\"Examples of convex polygons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/examples-of-convex-polygons.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/examples-of-convex-polygons-300x189.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In geometry, a polygon is a flat or plane, two-dimensional, closed shape bounded with straight sides, with at least three sides and angles. All polygons can be broadly divided into two groups based on the measure of their internal angles: convex and concave. Just like a convex mirror, a convex polygon curves outward. Let us learn more about the convex polygon, its formula, properties, types, and examples.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-definition-of-a-convex-polygon\">Definition of a Convex Polygon<\/h3>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-96e4ffac-94a8-47b3-ace4-92eec1e57c91\">\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Convex polygon is defined as a closed figure having all the interior angles less than <\/strong>$180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This means that all the vertices of the polygon will point outwards, away from the interior of the shape. No sides are pointing inward. A triangle is considered an important convex polygon. Other convex polygon shapes are quadrilateral, pentagon, hexagon, parallelogram, etc.<\/p>\n\n\n<\/div>\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"401\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/convex-polygon-shapes.png\" alt=\"Convex polygon shapes\" class=\"wp-image-34559\" title=\"Convex polygon shapes\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/convex-polygon-shapes.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/convex-polygon-shapes-300x194.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 eplus-wrapper\" id=\"2-properties-of-a-convex-polygon\">Properties of a Convex Polygon<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The diagonals of a convex polygon lie inside the polygon.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The internal angles of a convex polygon are always less than $180^\\circ$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">A polygon is considered convex if the line connecting every pair of its points lies entirely within it.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The sum of the interior angles of a convex polygon of sides \u201cn\u201d is given as $180(n\\;-\\;2)^\\circ$.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">To calculate the area of the convex polygon, the polygon is divided into triangles and then the area of each triangle is summed up.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-types-of-convex-polygons\">Types of Convex Polygons<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Convex polygons can be divided into two types. They are as follows:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">1. Regular convex polygon<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">2. Irregular convex polygon<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-regular-convex-polygon\">Regular Convex Polygon<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A regular convex polygon (or a convex regular polygon) is one with equal sides and congruent interior angles that are less than 180 degrees. In a regular polygon, the vertices are equidistant from the center.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"395\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-of-a-regular-convex-polygon-square.png\" alt=\"Example of a regular convex polygon - square\" class=\"wp-image-34560\" title=\"Example of a regular convex polygon - square\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-of-a-regular-convex-polygon-square.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-of-a-regular-convex-polygon-square-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-irregular-convex-polygon\">Irregular Convex Polygon<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Each side of an irregular convex polygon has a different length, and all of the internal angles have different measurements.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"335\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-of-a-convex-irregular-polygon.png\" alt=\"Example of a convex irregular polygon\" class=\"wp-image-34561\" title=\"Example of a convex irregular polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-of-a-convex-irregular-polygon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-of-a-convex-irregular-polygon-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-interior-angles-of-a-convex-polygon\">Interior Angles of a Convex Polygon<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The interior angles of a polygon are the angles inside the polygon. A polygon has the same number of interior angles as its sides.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-exterior-angles-of-a-convex-polygon\">Exterior Angles of a Convex Polygon<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The exterior angles of a polygon are the angles formed by extending the sides of a polygon. The sum of the exterior angles of a polygon is $360^\\circ$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"427\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/interior-and-exterior-angles-of-a-convex-pentagon.png\" alt=\"Interior and exterior angles of a convex pentagon\" class=\"wp-image-34562\" title=\"Interior and exterior angles of a convex pentagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/interior-and-exterior-angles-of-a-convex-pentagon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/interior-and-exterior-angles-of-a-convex-pentagon-300x207.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-convex-polygon-formulas\">Convex Polygon Formulas<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s see some formulas related to convex polygons.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"9-perimeter-of-regular-convex-polygon\">Perimeter of Regular Convex Polygon<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The total distance of the outer sides of a closed figure is known as the perimeter. It is the total length of all sides of a polygon. A regular polygon has all sides equal. Therefore, we can find the perimeter of a regular polygon by repeated addition.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula to calculate the perimeter of regular convex polygon is as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter $= n \\times s$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Where, $n =$ Number of sides<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $s =$ Length of sides<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"10-perimeter-of-irregular-convex-polygon\">Perimeter of Irregular Convex Polygon<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is the total distance around a polygon. It can be found by adding together all the sides of the polygon.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula to calculate the perimeter of irregular convex polygon is as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter $=$ Sum of all sides<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"11-sum-of-interior-angles-of-a-convex-polygon\">Sum of Interior Angles of a Convex Polygon<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The sum of interior angles of a convex polygon with \u201cn\u201d sides is given by the formula,&nbsp; 180(n-2).&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, a square has 4 sides. Thus, $n = 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the sum of its interior angles $= 180^\\circ (4\\;-\\;2) = 360^\\circ$.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"12-sum-of-exterior-angles-of-a-convex-polygon\">Sum of Exterior Angles of a Convex Polygon<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Sum of exterior angles of a polygon is $360^\\circ$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Each exterior angle of a convex polygon is equal to $\\frac{360^\\circ}{n}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here \u201cn\u201d is the number of sides of the polygon.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, a square has 4 sides. So each exterior angle is&nbsp; $\\frac{360^\\circ}{4}$, which is equal to $90^\\circ$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-difference-between-concave-polygon-and-convex-polygon\">Difference between Concave Polygon and Convex Polygon<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Take a look at the image given below to see the real life examples of convex and concave polygons.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"334\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/real-life-example-of-concave-vs-convex-polygon.png\" alt=\"Real-life example of concave vs convex polygon\" class=\"wp-image-34563\" title=\"Real-life example of concave vs convex polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/real-life-example-of-concave-vs-convex-polygon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/real-life-example-of-concave-vs-convex-polygon-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The difference between a concave and convex polygon are as follows:<\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><thead><tr><th><strong>&nbsp; &nbsp; Convex Polygon<\/strong><\/th><th><strong>Concave Polygon<\/strong><\/th><\/tr><\/thead><tbody><tr><td>A convex polygon has all its interior angles less than 180 degrees.<\/td><td>A concave polygon has at least one interior angle more than 180 degrees.<\/td><\/tr><tr><td>A convex polygon has no diagonal in the exterior.<br><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-7-1.png\" alt=\"Diagonals of a convex polygon lying inside the polygon\"><\/td><td>Concave polygons have portions of diagonals in the exterior.<br><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-7-2.png\" alt=\"One diagonal lying outside the concave polygon\"><\/td><\/tr><tr><td>All sides point outwards. There are no dents.&nbsp;<\/td><td>Some sides point inward. There are dents.<\/td><\/tr><tr><td>The line joining any two vertices of the convex polygon lies completely within it.<\/td><td>A line joining two vertices of a concave polygon may or may not lie within the polygon.<\/td><\/tr><tr><td>Convex polygons can be regular or irregular.<\/td><td>Concave polygons are never regular.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"14-facts-about-convex-polygon\">Facts about Convex Polygon<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Convex polygon is defined as a polygon with all its interior angles less than or equal to 180 degree.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Based on the shape of the polygon, the types of a polygon are convex and concave, regular and irregular, simple and complex.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A regular polygon in geometry is always a convex polygon.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Convex polygons are easier to draw in comparison to concave polygons.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The sum of the interior angles of a convex polygon is by the formula $180(n\\;-\\;2)^\\circ$.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The sum of the exterior angles of a convex polygon is given as $\\frac{360^\\circ}{n}$.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"15-solved-examples-on-convex-polygon\">Solved Examples on Convex Polygon<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Find the perimeter of the regular decagon if the length of the side is 10 in.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Decagon is a regular polygon with 10 sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$s = 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$n = 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of convex polygon$ = n \\times s$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, Perimeter $= 10 \\times 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 100$ in.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. What is the measure of an interior angle of a regular convex polygon like a hexagon?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The number of sides of a hexagon is $n = 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the formula for the&nbsp; sum of all interior angles of a polygon of n sides is<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$180 (n\\;-\\;2)^\\circ$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the sum of the interior angles of the hexagon is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$180 \\times (6\\;-\\;2)^\\circ = 180 \u00d7 (4)^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 720^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the given hexagon is regular, all 6 interior angles measure the same. Therefore, the measure of each interior angle is $\\frac{720}{6} = 120^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the required angle $= 120^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. The interior angles of a pentagon are <\/strong>$x^\\circ,\\; x^\\circ,\\; 2x^\\circ,\\; 2x^\\circ$<strong> and <\/strong>$3x^\\circ$<strong>. What is x ?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that, a pentagon has 5 sides and has interior angles that sum to $(5 \\;-\\; 2) \\times 180^\\circ = 540^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Writing the equation for the above example,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x^\\circ +&nbsp;x^\\circ + 2x^\\circ + 2x^\\circ + 3x^\\circ = 540^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$9x^\\circ = 540^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$x&nbsp; = \\frac{540}{9}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$x&nbsp; = 60^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Find the value of x in the given figure:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"311\" height=\"301\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/measures-of-exterior-angles-of-a-triangle.png\" alt=\"Measures of exterior angles of a triangle\" class=\"wp-image-34564\" title=\"Measures of exterior angles of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/measures-of-exterior-angles-of-a-triangle.png 311w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/measures-of-exterior-angles-of-a-triangle-300x290.png 300w\" sizes=\"auto, (max-width: 311px) 100vw, 311px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that, sum of exterior angles of a polygon is $360^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $110^\\circ + 120^\\circ + x = 360^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$230^\\circ +&nbsp; x^\\circ = 360^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;$x^\\circ = 360^\\circ \\;-\\;&nbsp; 230^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;$x^\\circ = 130^\\circ$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"16-practice-problems-on-convex-polygon\">Practice Problems on Convex Polygon<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Convex Polygon - Definition, Formula, Properties, Types, Examples<\/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\">The name of the four sided regular convex polygon is ________________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Rectangle<\/div><div class=\"spq_answer_block\" data-value=\"1\">Square<\/div><div class=\"spq_answer_block\" data-value=\"2\">Parallelogram<\/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: Square<br\/>A regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equivalent and less than $180^\\circ$. Thus, square is a regular convex polygon<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the type of a polygon represented by the three polygons in the following image?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-pp1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">Regular concave polygon<\/div><div class=\"spq_answer_block\" data-value=\"1\">Irregular concave polygon<\/div><div class=\"spq_answer_block\" data-value=\"2\">Regular convex polygon<\/div><div class=\"spq_answer_block\" data-value=\"3\">Irregular convex polygon<\/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: Regular convex polygon<br\/>The image shows a triangle with three equal interior angles, a square and a regular hexagon.<br>\r\nA regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equal and less than $180^\\circ$.<\/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\">Each interior angle of a convex polygon is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$greater than 80^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$less than 90^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$greater than 180^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$less than 180^\\circ$<\/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: $less than 180^\\circ$<br\/>A convex polygon is a polygon with all interior angles less than $180^\\circ$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Each exterior angle of the square is  _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">180 degrees<\/div><div class=\"spq_answer_block\" data-value=\"1\">360 degrees<\/div><div class=\"spq_answer_block\" data-value=\"2\">270 degrees<\/div><div class=\"spq_answer_block\" data-value=\"3\">90 degrees<\/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: 90 degrees<br\/>Each exterior angle of a convex polygon is equal to $\\frac{360^\\circ}{n}$. Here, \u201cn\u201d is the number of sides of the polygon. A square has 4 sides. So, each exterior angle is $\\frac{360^\\circ}{4}$, which is equal to $90^\\circ$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Three geometric shapes are given below. Which figure is convex?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-pp2.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">Figure 1<\/div><div class=\"spq_answer_block\" data-value=\"1\">Figure 2<\/div><div class=\"spq_answer_block\" data-value=\"2\">Figure 3<\/div><div class=\"spq_answer_block\" data-value=\"3\">All 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: Figure 1<br\/>Convex polygon is defined as a closed figure having all the interior angles less than 180. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Thus, only figure 1 is a convex 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\": \"Convex Polygon - Definition, Formula, Properties, Types, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Convex Polygon\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The name of the four sided regular convex polygon is ________________.\",\n                    \"text\": \"The name of the four sided regular convex polygon is ________________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equivalent and less than $$180^\\\\circ$$. Thus, square is a regular convex polygon\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Rectangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equivalent and less than $$180^\\\\circ$$. Thus, square is a regular convex polygon\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Parallelogram\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equivalent and less than $$180^\\\\circ$$. Thus, square is a regular convex polygon\"\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\": \"A regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equivalent and less than $$180^\\\\circ$$. Thus, square is a regular convex polygon\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Square\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equivalent and less than $$180^\\\\circ$$. Thus, square is a regular convex polygon\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equivalent and less than $$180^\\\\circ$$. Thus, square is a regular convex polygon\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the type of a polygon represented by the three polygons in the following image?\",\n                    \"text\": \"What is the type of a polygon represented by the three polygons in the following image? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-pp1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The image shows a triangle with three equal interior angles, a square and a regular hexagon.<br>\r\nA regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equal and less than $$180^\\\\circ$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Regular concave polygon\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The image shows a triangle with three equal interior angles, a square and a regular hexagon.<br>\r\nA regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equal and less than $$180^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Irregular concave polygon\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The image shows a triangle with three equal interior angles, a square and a regular hexagon.<br>\r\nA regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equal and less than $$180^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Irregular convex polygon\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The image shows a triangle with three equal interior angles, a square and a regular hexagon.<br>\r\nA regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equal and less than $$180^\\\\circ$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Regular convex polygon\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The image shows a triangle with three equal interior angles, a square and a regular hexagon.<br>\r\nA regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equal and less than $$180^\\\\circ$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The image shows a triangle with three equal interior angles, a square and a regular hexagon.<br>\r\nA regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equal and less than $$180^\\\\circ$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Each interior angle of a convex polygon is\",\n                    \"text\": \"Each interior angle of a convex polygon is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A convex polygon is a polygon with all interior angles less than $$180^\\\\circ$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$greater than 80^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A convex polygon is a polygon with all interior angles less than $$180^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$less than 90^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A convex polygon is a polygon with all interior angles less than $$180^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$greater than 180^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A convex polygon is a polygon with all interior angles less than $$180^\\\\circ$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$less than 180^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A convex polygon is a polygon with all interior angles less than $$180^\\\\circ$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A convex polygon is a polygon with all interior angles less than $$180^\\\\circ$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Each exterior angle of the square is  _________.\",\n                    \"text\": \"Each exterior angle of the square is  _________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Each exterior angle of a convex polygon is equal to $$\\\\frac{360^\\\\circ}{n}$$. Here, \u201cn\u201d is the number of sides of the polygon. A square has 4 sides. So, each exterior angle is $$\\\\frac{360^\\\\circ}{4}$$, which is equal to $$90^\\\\circ$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"180 degrees\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Each exterior angle of a convex polygon is equal to $$\\\\frac{360^\\\\circ}{n}$$. Here, \u201cn\u201d is the number of sides of the polygon. A square has 4 sides. So, each exterior angle is $$\\\\frac{360^\\\\circ}{4}$$, which is equal to $$90^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"360 degrees\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Each exterior angle of a convex polygon is equal to $$\\\\frac{360^\\\\circ}{n}$$. Here, \u201cn\u201d is the number of sides of the polygon. A square has 4 sides. So, each exterior angle is $$\\\\frac{360^\\\\circ}{4}$$, which is equal to $$90^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"270 degrees\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Each exterior angle of a convex polygon is equal to $$\\\\frac{360^\\\\circ}{n}$$. Here, \u201cn\u201d is the number of sides of the polygon. A square has 4 sides. So, each exterior angle is $$\\\\frac{360^\\\\circ}{4}$$, which is equal to $$90^\\\\circ$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"90 degrees\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Each exterior angle of a convex polygon is equal to $$\\\\frac{360^\\\\circ}{n}$$. Here, \u201cn\u201d is the number of sides of the polygon. A square has 4 sides. So, each exterior angle is $$\\\\frac{360^\\\\circ}{4}$$, which is equal to $$90^\\\\circ$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Each exterior angle of a convex polygon is equal to $$\\\\frac{360^\\\\circ}{n}$$. Here, \u201cn\u201d is the number of sides of the polygon. A square has 4 sides. So, each exterior angle is $$\\\\frac{360^\\\\circ}{4}$$, which is equal to $$90^\\\\circ$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Three geometric shapes are given below. Which figure is convex?\",\n                    \"text\": \"Three geometric shapes are given below. Which figure is convex? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-pp2.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Convex polygon is defined as a closed figure having all the interior angles less than 180. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Thus, only figure 1 is a convex polygon.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Figure 2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Convex polygon is defined as a closed figure having all the interior angles less than 180. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Thus, only figure 1 is a convex polygon.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Figure 3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Convex polygon is defined as a closed figure having all the interior angles less than 180. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Thus, only figure 1 is a convex polygon.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"All of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Convex polygon is defined as a closed figure having all the interior angles less than 180. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Thus, only figure 1 is a convex polygon.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Figure 1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Convex polygon is defined as a closed figure having all the interior angles less than 180. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Thus, only figure 1 is a convex polygon.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Convex polygon is defined as a closed figure having all the interior angles less than 180. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Thus, only figure 1 is a convex polygon.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"17-frequently-asked-questions-on-convex-polygons\">Frequently Asked Questions on Convex Polygons<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\" 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-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\"><strong>What are some real-life examples of convex polygons?<\/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-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Convex polygons can be seen in everyday life in our surroundings. Some real-life examples include stop signs on the roads, hexagons and pentagons on a football, a coin, etc.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"508\" height=\"136\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-FAQ-1.png\" alt=\"convex polygon examples in real life.\" class=\"wp-image-28293\" title=\"convex polygon examples in real life.\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-FAQ-1.png 508w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-FAQ-1-300x80.png 300w\" sizes=\"auto, (max-width: 508px) 100vw, 508px\" \/><\/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-1-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\"><strong>How do you tell whether the polygon is concave or convex?<\/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-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If a line drawn that passes through the polygon passes through only two sides, then the shape of the polygon is convex. On the other hand, if you can draw a line that can pass through more than two sides, it is a concave polygon. In 3-dimensional shapes, the same test can be performed to differentiate between the two.<\/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-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\"><strong>What are simple and complex polygons?<\/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-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A simple polygon has only one boundary, and it doesn&#8217;t cross over itself. The sides of a simple polygon do not intersect. A complex polygon is a polygon whose sides cross over each other one or more times.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"322\" height=\"142\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-FAQ-2.png\" alt=\"Example of a simple and complex polygon\" class=\"wp-image-28294\" title=\"Example of a simple and complex polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-FAQ-2.png 322w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/convex-polygon-FAQ-2-300x132.png 300w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/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-3-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\"><strong>Is a triangle a convex or 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-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A polygon is convex if all the interior angles are less than 180 degrees. If one or more of the interior angles is more than 180 degrees, the polygon is concave. A triangle is a geometric shape with three sides. In a triangle, the sum of all interior angles is itself 180\u00b0. Thus, a triangle is a convex 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-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\"><strong>Can a concave polygon be 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-4-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">No. In concave polygon, interior angle measures greater than $180^\\circ$ and one diagonal lies outside the polygon. In regular polygons, all sides are equal in length and all the interior angles are of equal measure. So, a concave polygon will not be 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-5-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\"><strong>Is a triangle convex or concave?<\/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-a2befc3d-345b-48e8-b00a-68dc6aee8c6f\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangle is always convex. A triangle can never be a concave polygon.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Convex Polygon? A convex polygon is a polygon with all interior angles less than $180^\\circ$ and vertices are pointed outwards.&nbsp; In convex polygons, all diagonals are in the interior of the polygon. All the vertices of a complex polygon point outwards. A regular polygon in geometry is always convex. Any closed shape &#8230; <a title=\"Convex Polygon &#8211; Definition, Formula, Properties, Types, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/convex-polygon\" aria-label=\"More on Convex Polygon &#8211; Definition, Formula, Properties, Types, Examples\">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-28282","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\/28282","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=28282"}],"version-history":[{"count":14,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28282\/revisions"}],"predecessor-version":[{"id":34565,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28282\/revisions\/34565"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=28282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=28282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=28282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}