CLASS-7
POLYGON - PENTAGON

PENTAGON -

A pentagon is a polygon with five sides and five angles. Here are a few key characteristics of pentagons:

Types of Pentagons:-

  1. Regular Pentagon:- All sides are equal in length.All internal angles are equal, with each angle measuring 108°. The regular pentagon is a symmetric shape often seen in geometry and art.
  2. Irregular Pentagon:- The sides and angles can have different lengths and measures. It does not have the symmetry of a regular pentagon.

Area Formula for a Regular Pentagon:-

The area A of a regular pentagon with side length s can be calculated using the formula:-

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     A = ------​ √5 (5 + 2√5​)​ ⋅ s²

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Alternatively, you can also calculate the area using the apothem (the distance from the center of the pentagon to the midpoint of one of its sides):

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   A = ------ × Perimeter × Apothem

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Examples of Pentagons in Real Life:-

  • The Pentagon building in Arlington, Virginia, which is the headquarters of the United States Department of Defense, is perhaps the most famous example of a pentagon-shaped structure.
  • Certain natural shapes, such as flowers or sea stars, often exhibit pentagonal symmetry.