Pentagons can be regular or irregular, depending on whether all sides are the same length. Now let\u2019s go through the main ways to calculate the perimeter of a pentagon.<\/p>\n
Perimeter of a Pentagon: Formulas From Basic Sum to Trigonometry<\/h2>\n
The perimeter of a pentagon is the total length around the shape. So, for a pentagon \\( ABCDE \\) shown in the figure below, we write:<\/p>\n
\\[
\nP=AB+BC+CD+DE+AE,
\n\\]<\/p>\n
where \\( P \\) is the perimeter<\/a>.<\/p>\n If the pentagon is regular, then all five sides are equal. In that case:<\/p>\n \\[ Note<\/strong>. If we label the side lengths as \\( a \\), \\( b \\), \\( c \\), \\( d \\), and \\( e \\), then the formulas can be written in a more familiar way: You can find the perimeter of a pentagon if the radius of the circumscribed circle is given (this radius is also called the circumradius).<\/p>\n Important<\/strong>: this method applies only to a regular pentagon inscribed in a circle.<\/p><\/blockquote>\n Here, the radius is the segment from the center \\( O \\) to a vertex. First, we find the side length:<\/p>\n \\[ Then we calculate the perimeter:<\/p>\n \\[ You can also calculate the perimeter of a pentagon if the apothem is known.<\/p>\n Note<\/strong>: this method also applies only to a regular pentagon.<\/p><\/blockquote>\n The apothem is a perpendicular segment drawn from the center of the pentagon to one of its sides (to the point where the inscribed circle touches the side). If the apothem is known, the side length can be found like this:<\/p>\n \\[ Once you have the side length, the perimeter is:<\/p>\n \\[ To better understand how to find the perimeter of a pentagon, let\u2019s work through a few examples. Each one includes a complete solution. However, it\u2019s a good idea to try the calculations on your own first\u2014and then check your answer.<\/p>\n For an irregular pentagon, add all five side lengths:<\/p>\n \\[ So, the perimeter is \\( 25 \\) cm.<\/p>\n Since the pentagon is regular:<\/p>\n \\[ So, the perimeter is \\( 50 \\) cm.<\/p>\n Use the perimeter formula for a regular pentagon:<\/p>\n \\[ So, the side length is \\( 5 \\) cm.<\/p>\n First, calculate the side length:<\/p>\n \\[ Then the perimeter is:<\/p>\n \\[ So, the perimeter is approximately \\( 29.39 \\) cm.<\/p>\n First, calculate the side length:<\/p>\n \\[ Then the perimeter is:<\/p>\n \\[ So, the perimeter is approximately \\( 36.33 \\) cm.<\/p>\n Want to reinforce the topic and quickly expand your understanding of pentagons? Here\u2019s a short list of resources that naturally complement this article:<\/p>\n If you enjoy not only calculating but also programming, try turning this flowchart into working code in your favorite language. It\u2019s a small task, but it\u2019s very practical. It helps you practice input handling, checks, branching (if\/else logic), and cleanly displaying the final result. And yes\u2014it\u2019s satisfying to see how a geometry formula becomes part of a real program.<\/p>\n Write your own version, test it with different values, and you\u2019ll quickly feel how the algorithm starts working in practice.<\/p>\n The perimeter of a pentagon is simply the sum of the lengths of all its sides. A pentagon is a<\/p>\n","protected":false},"author":1,"featured_media":2917,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"template-centered.php","format":"standard","meta":{"footnotes":""},"categories":[198],"tags":[436,460,474,461,463],"class_list":["post-2900","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-area-and-perimeter","tag-geometry","tag-pentagon","tag-perimeter-of-a-pentagon","tag-polygons","tag-regular-pentagon"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/posts\/2900","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/comments?post=2900"}],"version-history":[{"count":16,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/posts\/2900\/revisions"}],"predecessor-version":[{"id":3023,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/posts\/2900\/revisions\/3023"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/media\/2917"}],"wp:attachment":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/media?parent=2900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/categories?post=2900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/tags?post=2900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"Image:](\"https:\/\/www.mathros.net.ua\/en\/wp-content\/uploads\/2023\/02\/pentagon-perimeter2.jpg\")
<\/p>\n
\nP=5 \\cdot AB.
\n\\]<\/p>\n![\"Image:](\"https:\/\/www.mathros.net.ua\/en\/wp-content\/uploads\/2023\/02\/pentagon-perimeter4.jpg\")
<\/p>\n
\n\\[
\nP = a + b + c + d + e,\\qquad P = 5\\cdot a.
\n\\]<\/p><\/blockquote>\nPerimeter of a Pentagon Using the Circumradius<\/h3>\n
![\"Image:](\"https:\/\/www.mathros.net.ua\/en\/wp-content\/uploads\/2023\/02\/pentagon-perimeter7.jpg\")
<\/p>\n
\nAB = 2\\cdot AO\\cdot \\sin\\left(\\frac{180^\\circ}{5}\\right)=2\\cdot AO\\cdot \\sin(36^\\circ).
\n\\]<\/p>\n
\nP=5\\cdot AB.
\n\\]<\/p>\nPerimeter of a Pentagon Using the Apothem<\/h3>\n
![\"Image:](\"https:\/\/www.mathros.net.ua\/en\/wp-content\/uploads\/2023\/02\/pentagon-perimeter9.jpg\")
<\/p>\n
\nAB = 2\\cdot OF\\cdot \\tan\\left(\\frac{180^\\circ}{5}\\right)=2\\cdot OF\\cdot \\tan(36^\\circ).
\n\\]<\/p>\n
\nP=5\\cdot AB.
\n\\]<\/p>\nPerimeter of a Pentagon: Examples with Answers<\/h2>\n
Example 1. Find the perimeter if the sides are 5 cm, 4 cm, 7 cm, 3 cm, and 6 cm<\/h3>\n
\nP=a+b+c+d+e=5+4+7+3+6=25.
\n\\]<\/p>\nExample 2. Find the perimeter of a regular pentagon with side length 10 cm<\/h3>\n
\nP=5\\cdot a=5\\cdot 10=50.
\n\\]<\/p>\nExample 3. If the perimeter of a regular pentagon is 25 cm, find one side length<\/h3>\n
\nP=5\\cdot a,\\qquad 25=5\\cdot a,\\qquad a=5.
\n\\]<\/p>\nExample 4. Find the perimeter of a regular pentagon inscribed in a circle with radius 5 cm<\/h3>\n
\nAB = 2\\cdot AO\\cdot \\sin(36^\\circ)=2\\cdot 5\\cdot 0.587785 \\approx 5.88.
\n\\]<\/p>\n
\nP=5\\cdot AB \\approx 5\\cdot 5.88 \\approx 29.39.
\n\\]<\/p>\nExample 5. Find the perimeter of a regular pentagon if the apothem OF=5 cm<\/h3>\n
\nAB=2\\cdot OF\\cdot \\tan(36^\\circ)=2\\cdot 5\\cdot 0.726543 \\approx 7.27.
\n\\]<\/p>\n
\nP=5\\cdot AB \\approx 5\\cdot 7.27 \\approx 36.33.
\n\\]<\/p>\nSee Also: Helpful Materials for Practice<\/h2>\n
\n
Geometry in Code: Turn a Flowchart into a Program<\/h2>\n
![\"Flowchart](\"https:\/\/www.mathros.net.ua\/en\/wp-content\/uploads\/2023\/02\/pentagon-perimeter19.jpg\")
<\/p>\n","protected":false},"excerpt":{"rendered":"