9514 1404 393
Answer:
84.3 square meters
Explanation:
A well-known formula for the area of a regular n-gon makes use of the perimeter (P) and the measure of the apothem (a), the distance from the center to one side. The ratio of half the length of one side to the apothem is the tangent of half the central angle of one triangle, so we have ...
(P/(2n))/a = tan(180°/n)
Then the apothem is ...
a = P/(2n·tan(180°/n))
The area formula tells you ...
A = (1/2)Pa
so this would give an area formula for an n-gon of ...
A = P²/(4n·tan(180°/n))
For a pentagon (n=5) with a perimeter of 35 m, the area is ...
A = (35 m)²/(4·5·tan(36°)) = 61.25 m²/tan(36°) ≈ 84.3 m²