Area of a Pentagon Formula

A pentagon is 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 the same as each other. Pentagons can be regular or irregular and convex or concave. A regular pentagon is one with all equal sides and angles. Its interior angles are 108 degrees and its exterior angles are 72 degrees. An irregular pentagon is a shape that does not have equal sides and/or angles and therefore do 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.

The Area of a Pentagon Formula is, A = $\frac{5}{2}$sa
Where,
s is the side of the pentagon.
a is the apothem length.

Solved Examples

Question 1: Find the area of a pentagon of side 10 cm and apothem length 5 cm ?
Solution:
Given,
s = 10 cm
a = 5 cm
Area of a pentagon
= $\frac{5}{2}$ sa
= $\frac{5}{2}$ $\times$ 10 $\times$ 5 cm2
= 125 cm2

Practise This Question

Rohan attends a test with multiple choice questions with no negative marking. There were fifty questions and each question had four marks for answering right. What is the sample space of marks that Rohan could score?