Question

find the area of the regular pentagon below by using the area formula for triangles. a = 8 inches and b = 10 inches *picture not drawn to scale

Explanation:

Step1: Recall the property of a regular pentagon

A regular pentagon can be divided into 5 congruent isosceles triangles.

Step2: Use the triangle - area formula

The area formula for a triangle is $A_{\triangle}=\frac{1}{2}\times base\times height$. Here, the base of each triangle is $b = 10$ inches and the height is $a = 8$ inches. So, $A_{\triangle}=\frac{1}{2}\times10\times8=40$ square inches.

Step3: Calculate the area of the pentagon

Since the pentagon is made up of 5 such congruent triangles, $A_{pentagon}=5\times A_{\triangle}=5\times40 = 200$ square inches.

Answer:

B. 200 in²