Question

A regular pentagon has an apothem of 7.3 inches and a perimeter of 53

inches. What is the area of the pentagon?

Answer 1

193.45 in2

Explanation:

A regular pentagon is a polygon with 5 equal sides. If the perimeter of the regular pentagon is 53, the length of its side is:

side = 53 / 5 = 10.6 inches

To find the area of the pentagon, we can use the following formula:

Area = apothem * perimeter /2

Area = 7.3 * 53 /2 = 193.45 in2

Other way we can find the area is dividing the pentagon in 5 regular triangles, where their base are the sides of the pentagon and their height are the apothem of the pentagon, then we sum the area of the 5 triangles:

Area of one triangle = b*h/2 = 10.6*7.3/2 = 38.69 in2

Area of pentagon = 5 * 38.69 = 193.45 in2

Answer 2

The area of the pentagon is 193.45 square inches.

Explanation:

In order to solve this question we need to use the appropriate formula for the pentagon's area shown below:

area = (p*a)/2

Where p is the perimeter for the pentagon and a is it's apothem.

area = (53*7.3)/2 square inches

area = 386.9/2 square inches

area = 193.45 square inches

The area of the pentagon is 193.45 square inches.