Question

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

pentagon with a side of 6 m (1 point)
A. 123.9 m²
B. 12.4 m²
C. 61.9 m²
D. 49.5 m²

Answer 1

61.9

Explanation:

center center is 72 degree for each triangle

the distance of center to the side h=3/tan 36=4.12,

area=5* (4.12*6)/2=61.94==61.9

Answer 2

The area of the regular pentagon:
`A=5* (s*a)/(2)` where s=6m, and a=3*tg 54°= 3*1.37=4.13 m
Explanation: 54° is a half of the inner angle of the pentagon. The interior angles of a pentagon add up to 540°. Each angle is 108°.
Finally: A=
`5* (6*4.13)/(2)`=61.93 m².
Answer: C) 61.9 m²