Question

A regular heptagon has a side of approximately 3.9 yd and an apothem of approximately 4.0 yd.

Find the area of the heptagon

Answer 1

54.6 square yards

Explanation:

For any regular polygon, the area of the polygon is given by:

`A_(regular~polygon)=(1)/(2)nsa`, where

• n is the number of sides of the polygon,
• s is the side length of the polygon, and
• a is the length of the apothem.

Heptagons are 7-sided polygons, so n=7.

The length of a side and the apothem are given, so substitute and calculate:

`A_(heptagon)=(1)/(2)(7)sa`

`A_(heptagon)=(1)/(2)(7)(3.9~yd)(4.0~yd)`

`A_(heptagon)=54.6 ~yd^2`