Question

What is the area of regular pentagon with a side of 12 inches? Round the answer to the nearest 10th.

Answer 1

The area would be 247.8 sq. in.

We start out finding the length of the apothem. The apothem of a regular polygon is given by


`A=\frac{s}{2\tan{((180)/(n))}}`

where s is the side length and n is the number of sides. Using our information, we have

`A=\frac{5}{2\tan{((180)/(5))}}=(5)/(2tan(36))=8.26`

Now we find the area of the polygon using the formula:
A = n(1/2)(b)(h), where n is the number of sides, b is the side length, and h is the length of the apothem:

A = 5(1/2)(8.26)(12) = 247.8