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

Answer:

$A=172.04\ in^2$

Step-by-step 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 :

$A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5} } }\ a^2$

Put a = 10

So,

$A=\dfrac{1}{4}\times \sqrt{5(5+2\sqrt{5} )} \times 10^2\\\\A=172.04\ in^2$

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