{"id":1533,"date":"2022-04-20T07:49:02","date_gmt":"2022-04-20T07:49:02","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1533"},"modified":"2024-02-18T17:11:16","modified_gmt":"2024-02-18T17:11:16","slug":"decagon-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/decagon","title":{"rendered":"Decagon &#8211; Definition With Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><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-a14fbfe3-c1ab-4432-ab91-cab37ae42bd8\" 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\/geometry\/decagon#0-what-is-a-decagon>What is a Decagon?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/decagon#1-decagon-definition>Decagon Definition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/decagon#12-area-of-a-regular-decagon>Area of a Regular Decagon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/decagon#14-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/decagon#15-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/decagon#16-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-decagon\">What is a Decagon?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We know that a two-dimensional closed figure having a finite number of sides is known as a polygon. The minimum number of sides required to make a polygon are three. The number of angles in a polygon depends on the number of sides of the polygon. Polygons can be four sided (parallelogram), five sided (pentagon) and so on.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A decagon is simply a ten-sided polygon.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"492\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/examples-of-polygons.png\" alt=\"Examples of polygons\" class=\"wp-image-40204\" title=\"Examples of polygons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/examples-of-polygons.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/examples-of-polygons-300x238.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the above image, different sided polygons are given.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">One such type of polygon is a decagon having 10 sides.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-decagon-definition\">Decagon Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In geometry, a polygon having ten sides or a ten-sided polygon is called a decagon or ten-gon. It also has ten vertices and ten angles.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"457\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decagon-or-10-sided-polygon.png\" alt=\"Decagon or 10-sided polygon\" class=\"wp-image-40205\" title=\"Decagon or 10-sided polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decagon-or-10-sided-polygon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decagon-or-10-sided-polygon-300x221.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the above image, there are 10 sides: AB, BC, CD, DE, EF, FG, GH, HI, IJ, and AJ.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">There are 10 angles.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Decagon interior angles: $\\angle\\text{ABC}$, $\\angle\\text{BCD}$, $\\angle\\text{CDE}$, $\\angle\\text{DEF}$, $\\angle\\text{EFG}$,$\\angle\\text{FGH}$, $\\angle\\text{GHI}$, $\\angle\\text{HIJ}$, $\\angle\\text{IJA}$, and $\\angle\\text{JAB}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">There are 10 vertices: A, B, C, D, E, F, G, H, I, and J.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-sum-of-interior-angles-of-a-decagon\">Sum of Interior Angles of a Decagon<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The sum of interior angles of a polygon $=(n$$-$$2) \\times 360^\\circ$ where n is the number of sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the number of sides, i.e., $n=10$ in a decagon<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The sum of interior angles of a decagon $=(10$$-$$2)\\times180^\\circ=8\\times180^\\circ=1440^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the sum of all the interior angles of a decagon $= 1440^\\circ$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-types-of-decagon\">Types of Decagon<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">There are three possible ways in which we can classify decagons that are given below:<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Regular and Irregular Decagons<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading eplus-wrapper\" id=\"4-regular-decagons\">Regular Decagons<\/h4>\n\n\n\n<p class=\"eplus-wrapper\">Decagons in which all the sides and angles are equal are known as regular decagons.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"404\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/regular-decagon.png\" alt=\"Regular decagon\" class=\"wp-image-40207\" title=\"Regular decagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/regular-decagon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/regular-decagon-300x195.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The characteristics of a regular decagon are as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">a. All the sides are equal in length and all the angles are equal in measure.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">b. Each interior angle of a regular decagon $= \\frac{1440^\\circ}{10}=144^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">c. Because the sum of exterior angles of a decagon = 360, each exterior angle of a decagon $=\\frac{360^\\circ}{10}=36^\\circ $<\/p>\n\n\n\n<p class=\"eplus-wrapper\">d. The central angle is a circle and circle forms $360^\\circ $. On drawing 10 diagonals, we get each central angle of a decagon $=\\frac{360^\\circ}{10}=36^\\circ $<\/p>\n\n\n\n<p class=\"eplus-wrapper\">e. A regular decagon can be inscribed inside a circle. Also, the circle and the decagon share the same center.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"616\" height=\"526\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-regular-decagon-inscribed-inside-a-circle.png\" alt=\"A regular decagon inscribed inside a circle.\" class=\"wp-image-40208\" title=\"A regular decagon inscribed inside a circle.\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-regular-decagon-inscribed-inside-a-circle.png 616w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-regular-decagon-inscribed-inside-a-circle-300x256.png 300w\" sizes=\"auto, (max-width: 616px) 100vw, 616px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading eplus-wrapper\" id=\"5-irregular-decagons\">Irregular Decagons<\/h4>\n\n\n\n<p class=\"eplus-wrapper\">Decagons in which sides and angles are not equal are known as irregular decagons. There should be at least two sides and angles that are different in measurement. Examples of an irregular decagon are given below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"371\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/examples-of-irregular-decagons.png\" alt=\"Examples of irregular decagons\" class=\"wp-image-40210\" title=\"Examples of irregular decagons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/examples-of-irregular-decagons.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/examples-of-irregular-decagons-300x180.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Convex and Concave Decagons<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading eplus-wrapper\" id=\"6-convex-decagons\">Convex Decagons<\/h4>\n\n\n\n<p class=\"eplus-wrapper\">Decagons in which all the interior angles are less than $180^\\circ $ is known as convex decagons. Or, a convex decagon is a decagon whose diagonals lie inside it.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"374\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/convex-decagon.png\" alt=\"Convex decagon\" class=\"wp-image-40212\" title=\"Convex decagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/convex-decagon.png 619w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/convex-decagon-300x181.png 300w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In the above figure, all the diagonals will lie inside the decagon.&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading eplus-wrapper\" id=\"7-concave-decagons\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Concave Decagons<\/h4>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Concave decagons are the decagons in which at least one interior angle is greater<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;than $180^\\circ $. Or, the decagons that have at least one diagonal that lies outside it are known as the concave decagons.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"454\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/concave-decagon.png\" alt=\"Concave decagon\" class=\"wp-image-40213\" title=\"Concave decagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/concave-decagon.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/concave-decagon-300x219.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In the above figure, $\\angle$AJI is greater than $180^\\circ $ and if we join the vertices A and C, the<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;diagonal will lie outside the decagon.&nbsp;<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Simple and Complex Decagons<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading eplus-wrapper\" id=\"8-simple-decagons\">Simple Decagons<\/h4>\n\n\n\n<p class=\"eplus-wrapper\">Simple decagons are the decagons in which no sides cross each other. Also, the diagonals don\u2019t cross each other. A simple decagon can be regular as well as irregular.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"463\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/simple-decagons.png\" alt=\"\" class=\"wp-image-40215\" title=\"Simple decagons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/simple-decagons.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/simple-decagons-300x224.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the above figure, the decagon is a simple decagon with no sides crossing themselves.&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading eplus-wrapper\" id=\"9-complex-decagons\">Complex Decagons<\/h4>\n\n\n\n<p class=\"eplus-wrapper\">Complex decagons are the decagons that are self intersecting and there are additional interior spaces.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"440\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/complex-decagon.png\" alt=\"Complex decagon\" class=\"wp-image-40216\" title=\"Complex decagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/complex-decagon.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/complex-decagon-300x213.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-number-of-triangles-and-lines-of-symmetry-in-a-decagon\">Number of Triangles and Lines of Symmetry in a Decagon<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">When we join one vertex to the remaining vertices of the decagon, we get 8 triangles. When we join all the vertices independently to each other, then we get $8 \\times 10 = 80$ triangles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"466\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/the-number-of-triangles-in-a-decagon.png\" alt=\"The number of triangles in a decagon\" class=\"wp-image-40217\" title=\"The number of triangles in a decagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/the-number-of-triangles-in-a-decagon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/the-number-of-triangles-in-a-decagon-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A regular decagon has 10 lines of symmetry.&nbsp;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"388\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/the-number-of-lines-of-symmetry-in-a-regular-decagon.png\" alt=\"The number of lines of symmetry in a regular decagon\" class=\"wp-image-40218\" title=\"The number of lines of symmetry in a regular decagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/the-number-of-lines-of-symmetry-in-a-regular-decagon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/the-number-of-lines-of-symmetry-in-a-regular-decagon-300x188.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Irregular decagons may or may not have any line of symmetry.&nbsp;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"440\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/lines-of-symmetry-in-irregular-decagon.png\" alt=\"Lines of symmetry in irregular decagon\" class=\"wp-image-40219\" title=\"Lines of symmetry in irregular decagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/lines-of-symmetry-in-irregular-decagon.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/lines-of-symmetry-in-irregular-decagon-300x213.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-number-of-diagonals-in-a-decagon\">Number of Diagonals in a Decagon<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The number of diagonals of a polygon $=\\frac{n(n-3)}{2}$ where $n$ is the number of sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the number of sides, i.e., $n=10$ in a decagon<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the number of diagonals in a decagon $=\\frac{10\\times7}{2}=35$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-area-of-a-regular-decagon\">Area of a Regular Decagon<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Area of a regular decagon is the space occupied between the boundary of the decagon. The formula for area of a decagon is given by: $\\frac{5a^2}{2}\\times\\sqrt{5+2}\\sqrt{5}$ where $a =$ length of the side of the decagon.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-decagon-facts\">Decagon Facts<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">All sides of a regular decagon are the same length.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Decagram is a regular star polygon. Its vertex positions are the same as the regular decagon.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">A skew decagon is a skew polygon. It has 10 vertices and edges but not existing on the same plane.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"14-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. <\/strong><strong>Find the perimeter of a regular decagon if the length of a side is 5 units?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: The number of sides of a decagon $= 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since, the decagon is regular. So, all sides will be equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perimeter $= 5\\times10 = 50$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. <\/strong><strong>What is the sum of the number of sides, vertices, and angles in an irregular decagon?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: Number of sides of an irregular decagon $= 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Number of vertices of an irregular decagon $= 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Number of angles of an irregular decagon $= 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Sum $= 10 + 10 + 10 = 30$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. The two interior angles of a decagon are given <\/strong><strong>200<\/strong><strong> and <\/strong><strong>250<\/strong><strong>. Which type of a decagon is it?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: Since, the two interior angles of the decagon given above are more than <strong>180<\/strong><strong> <\/strong>so, it is called a concave decagon.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. How many lines of symmetry does a regular decagon have?&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: A regular decagon has 10 lines of symmetry.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"330\" height=\"338\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/lines-of-symmetry-of-a-regular-decagon.png\" alt=\"Lines of symmetry of a regular decagon\" class=\"wp-image-40220\" title=\"Lines of symmetry of a regular decagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/lines-of-symmetry-of-a-regular-decagon.png 330w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/lines-of-symmetry-of-a-regular-decagon-293x300.png 293w\" sizes=\"auto, (max-width: 330px) 100vw, 330px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"15-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Decagon - Definition With Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following is not a decagon?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-1-2.png\" alt=\"A\"><\/div><div class=\"spq_answer_block\" data-value=\"1\">B<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-2-2.png\" alt=\"B\"><\/div><div class=\"spq_answer_block\" data-value=\"2\">C<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-3-2.png\" alt=\"C\"><\/div><div class=\"spq_answer_block\" data-value=\"3\">D<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4.png\" alt=\"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: D<br\/>The number of sides in option D are 9. So, it is not a decagon.<\/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\">Fill in the blanks:<br>A regular decagon has all sides _________ and the measure of each angle of a regular decagon is _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">different; $36^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">different; $144^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">same; $144^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">same; $36^\\circ$<\/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: same; $144^\\circ$<br\/>The sides of a regular decagon are equal and the measure of each angle $=\\frac{1440^\\circ}{10} = 144^\\circ$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following is false for a regular decagon?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Each central angle measures $36^\\circ$.<\/div><div class=\"spq_answer_block\" data-value=\"1\">The sum of all angles of a decagon $= 1340^\\circ$.<\/div><div class=\"spq_answer_block\" data-value=\"2\">All the sides are equal.<\/div><div class=\"spq_answer_block\" data-value=\"3\">t has 10 lines of symmetry.<\/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: The sum of all angles of a decagon $= 1340^\\circ$.<br\/>The sum of all angles of a decagon $=(n$$-$$2)\\times360^\\circ=1440^\\circ$<\/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\": \"Decagon - Definition With Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Decagon - Definition With Examples\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is not a decagon?\",\n                    \"text\": \"Which of the following is not a decagon?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The number of sides in option D are 9. 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So, it is not a decagon.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"C <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-3-2.png\\\"\/>\",\n                                \n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The number of sides in option D are 9. So, it is not a decagon.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"D\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The number of sides in option D are 9. So, it is not a decagon.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The number of sides in option D are 9. So, it is not a decagon.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Fill in the blanks:<br>A regular decagon has all sides _________ and the measure of each angle of a regular decagon is _________.\",\n                    \"text\": \"Fill in the blanks:<br>A regular decagon has all sides _________ and the measure of each angle of a regular decagon is _________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The sides of a regular decagon are equal and the measure of each angle $$=\\\\frac{1440^\\\\circ}{10} = 144^\\\\circ$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"different; $$36^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sides of a regular decagon are equal and the measure of each angle $$=\\\\frac{1440^\\\\circ}{10} = 144^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"different; $$144^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sides of a regular decagon are equal and the measure of each angle $$=\\\\frac{1440^\\\\circ}{10} = 144^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"same; $$36^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sides of a regular decagon are equal and the measure of each angle $$=\\\\frac{1440^\\\\circ}{10} = 144^\\\\circ$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"same; $$144^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The sides of a regular decagon are equal and the measure of each angle $$=\\\\frac{1440^\\\\circ}{10} = 144^\\\\circ$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The sides of a regular decagon are equal and the measure of each angle $$=\\\\frac{1440^\\\\circ}{10} = 144^\\\\circ$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is false for a regular decagon?\",\n                    \"text\": \"Which of the following is false for a regular decagon?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The sum of all angles of a decagon $$=(n$$$$-$$$$2)\\\\times360^\\\\circ=1440^\\\\circ$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Each central angle measures $$36^\\\\circ$$.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of all angles of a decagon $$=(n$$$$-$$$$2)\\\\times360^\\\\circ=1440^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"All the sides are equal.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of all angles of a decagon $$=(n$$$$-$$$$2)\\\\times360^\\\\circ=1440^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"t has 10 lines of symmetry.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of all angles of a decagon $$=(n$$$$-$$$$2)\\\\times360^\\\\circ=1440^\\\\circ$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"The sum of all angles of a decagon $$= 1340^\\\\circ$$.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The sum of all angles of a decagon $$=(n$$$$-$$$$2)\\\\times360^\\\\circ=1440^\\\\circ$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The sum of all angles of a decagon $$=(n$$$$-$$$$2)\\\\times360^\\\\circ=1440^\\\\circ$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"16-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-53c0ae99-7619-427c-ad99-82984bea2925\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n\n<div style=\"border-color:#f1f1f1\" class=\"wp-block-ub-content-toggle-panel wp-block-ub-content-toggle-accordion\"><div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color:#f1f1f1\"><span class=\"wp-block-ub-content-toggle-accordion-title\" style=\"color:#000000\"><strong>What is the difference between a decagon and a dodecagon?<\/strong><\/span><span class=\"wp-block-ub-content-toggle-accordion-state-indicator dashicons dashicons-arrow-right-alt2 \"><\/span><\/div><div style=\"height:0;padding-top:0;padding-bottom:0\" class=\"wp-block-ub-content-toggle-accordion-content-wrap\">\n<p class=\"eplus-wrapper\">A decagon is a polygon with ten sides, ten vertices, and ten angles. On the other hand, a dodecagon is a polygon with twelve sides, twelve vertices, and twelve angles.<\/p>\n<\/div><\/div>\n\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-1-53c0ae99-7619-427c-ad99-82984bea2925\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-53c0ae99-7619-427c-ad99-82984bea2925\"><strong>Can we find decagons in real life?<\/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-1-53c0ae99-7619-427c-ad99-82984bea2925\">\n\n<p class=\"eplus-wrapper\">Decagons can be seen in various things in the surroundings, such as coasters, coins, umbrellas, drums, watches, cutlery, etc. Also, a decagon is an intriguing form of polygons and is widely used while doing wall art.<\/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-2-53c0ae99-7619-427c-ad99-82984bea2925\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-53c0ae99-7619-427c-ad99-82984bea2925\"><strong>What is the history of a decagon?<\/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-2-53c0ae99-7619-427c-ad99-82984bea2925\">\n\n<p class=\"eplus-wrapper\">The word \u201cdecagon\u201d dates back to the sixteenth century, and is derived from the Latin word decagonum, wherein deca means ten and gonum means angles. So, the word decagon means ten angles.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What is a Decagon? We know that a two-dimensional closed figure having a finite number of sides is known as a polygon. The minimum number of sides required to make a polygon are three. The number of angles in a polygon depends on the number of sides of the polygon. Polygons can be four sided &#8230; <a title=\"Decagon &#8211; Definition With Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/decagon\" aria-label=\"More on Decagon &#8211; Definition With 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-1533","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\/1533","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=1533"}],"version-history":[{"count":17,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1533\/revisions"}],"predecessor-version":[{"id":40221,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1533\/revisions\/40221"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}