How to Find the Area of Pentagon? Explain With Examples

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A pentagon is a five-sided polygon in geometry. It may be simple or self – intersecting in shape. The five angles present in the Pentagon are equal. A regular pentagon has all of the sides and angles are equal. Pentagons can be regular or irregular and convex or concave. A regular pentagon is one with all equal sides and angles. Its interior angles measure 108 degrees and its exterior angles measure 72 degrees. An irregular pentagon is a shape that does not have equal sides and/or angles and therefore does not have specified angles. A convex pentagon is one whose vertices, or points, where the sides meet, is pointing outwards as opposed to a concave pentagon whose vertices point inwards. Imagine a collapsed roof of a house. Now, the Pentagon area is derived by multiplying side and apothem length with (5/2). To learn more about the area of pentagon along with the details of apothem and other related terms, check the linked article.

Area of a Pentagon

The area of the Pentagon is the area that is within the sides of the Pentagon. To calculate the area of the Pentagon we can use the area of an isosceles triangle. We divide the area of the Pentagon into five isosceles triangles and calculate it accordingly. The formula for the area of the Pentagon in terms of side (s), apothem (a) the area is 5/2 × s × a, where a is the apothem length, and s is the side of the Pentagon.

Area of a Pentagon Formula

The area of the Pentagon is equal to 5/2 times the apothem length and of the side of the Pentagon.

The formula for the area of the Pentagon is the 5/2 × s × a.

also, Area of a pentagon,

A =14√5(5+2√5)s2

where ‘s’ is the length of the side of the Pentagon and a is the apothem of a pentagon.

Calculation of Area of Pentagon

The area of a Pentagon is 5/2 × s × a. By following the steps mentioned below we can find the area of the Pentagon.

  • Step 1: Calculate the length of the side of the Pentagon.
  • Step 2: Find the apothem length of the pentagon.
  • Step 3: Find out the product of the 5/2 times the apothem length and of the side of the Pentagon. This will give the area of the Pentagon.
  • Step 4: Represent the answer in square units.

Summary

Pentagon is an important geometric shape vastly applied in fields like designing, graphics, architecture, construction, etc. It is helpful to relate to various designs and to build structures and artworks. It is crucial for students to have knowledge of its properties, and dimensions as it enables them to understand their applications. Cuemath offers interactive math resources for students to efficiently learn math concepts. To find some of the best math learning resources, visit website and learn more.


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