Question

Find the area of the regular polygon. Give the answer to the nearest tenth.

pentagon with radius 8 m

A) 304.3 m2
B) 152.2 m2
C) 30.4 m2
D) 154.2 m2

Answer 1

use the formula (x-2)x180 to find the sum of interior angles which wold be equal to 540 deg
divide the pentagon into five triangles with interior angle 108 degrees
apply 1/2 (8)(8) sin 108 to find the area of 1 triangle
=30.43 m ^2
multiply this answer with 5 to get the area of pentagon
152.17 m^2
therefore 152.2 m^2
answer is B

Answer 2

why would it need to be equal to 540 degrees?

Answer 3

okay it doesn't need to be it just is gotcha

Answer 4

The area of a regular polygon of n sides inscribed in a circle of radius r is \[\text{Area}= n r^2 \text{Cos}\left[\frac{\pi }{n}\right] \text{Sin}\left[\frac{\pi }{n}\right]\]=\[80 \sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}} \left(1+\sqrt{5}\right)=152.169 \]