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
...(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](https://tex.z-dn.net/?f=p%3D7%5Ctimes%207.7)
![p=53.9](https://tex.z-dn.net/?f=p%3D53.9)
Substituting p=53.9 and a=8 in (i), we get
![A=\dfrac{1}{2}(53.9)(8)](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B1%7D%7B2%7D%2853.9%29%288%29)
![A=(53.9)(4)](https://tex.z-dn.net/?f=A%3D%2853.9%29%284%29)
![A=215.6](https://tex.z-dn.net/?f=A%3D215.6)
Therefore, the area of the regular polygon is 215.6 m².