Question

How do I do this? Anyone help!

Answer 1

Given:

Number of sides = 7

Apothem = 8 meters

Side length = 7.7 meters

To find:

The area of the regular polygon.

Solution:

We know that,

Area of a regular polygon is

$A=\dfrac{1}{2}pa$        ...(i)

where, p is perimeter and a is apothem.

Perimeter of a regular polygon is the product of number of sides and side length.

$p=7\times 7.7$

$p=53.9$

Substituting p=53.9 and a=8 in (i), we get

$A=\dfrac{1}{2}(53.9)(8)$

$A=(53.9)(4)$

$A=215.6$

Therefore, the area of the regular polygon is 215.6 m².