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 measures 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 a pentagon along with the details of apothem and other related terms, check the linked article.
Area Formula for a Pentagon
The Area of a Pentagon Formula is,
| A = (5 ⁄ 2) × s × a |
Where,
- “s” is the side of the Pentagon
- “a” is the apothem length
Example Question Using Pentagon Area Formula
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 = A = (5 ⁄ 2) × s × a
= (5 ⁄ 2) × 10 × 5 cm2
= 125 cm2.
Find the area of the given pentagon ABCDE in which each one of BF, CH and EG is perpendicular to AD such that AF = 9 cm, AG = 13 cm, AH = 19 cm, AD = 24 cm, BF = 6 cm, CH = 8 cm and EG = 9 cm