Question

What is the area of a regular pentagon with a side length of 10 inches and a distance from the center to a vertex of 10 inches? Round your answer to the nearest tenth.

Answer 1

`A=172.04\ in^2`

Explanation:

Given that,

The side length of a regular pentagon = 10 inches

The distance from the center to a vertex of 10 inches

The formula for the area of a regular pentagon is given by :

`A=(1)/(4)\sqrt{5(5+2√(5) } }\ a^2`

Put a = 10

So,

`A=(1)/(4)* \sqrt{5(5+2√(5) )} * 10^2\\\\A=172.04\ in^2`

So, the area of a regular pentagon is equal to
`172.04\ in^2`.