Question

The area of the regular pentagon is 6.9 cm2. What is the perimeter? 2 cm 5 cm 10 cm 20 cm

Answer 1

we know that

The formula to find the area of a regular polygon is given by

`A=(S^(2)*n)/(4*tan((180)/(n)))`

where

s is the length of the side

n is the number of sides

In this problem we have

`A=6.9\ cm^(2) \\ n=5`

Solve for S

Find the length of the side of the regular pentagon

`S^(2) =(1)/(n) *[A*4*tan(180/n)]\\ \\ S^(2) =(1)/(5) *[6.9*4*tan(180/5)]\\ \\ S^(2)=4.01\\ \\ S=2\ cm`

Find the perimeter of the regular pentagon

`Perimeter=5*2=10\ cm`

therefore

the answer is

the perimeter of the regular pentagon is
`10\ cm`