Question

find the area of the regular pentagon below by using the area formula for triangles. a = 4 inches and b = 6 inches picture not drawn to scale a. 10 in² b. 120 in² c. 60 in² d. 24 in²

Explanation:

Step1: Recall triangle area formula

The area formula for a triangle is $A_{triangle}=\frac{1}{2}ab$, where $a$ is the base and $b$ is the height.

Step2: Find area of one triangle

Given $a = 4$ inches and $b=6$ inches. Substitute into the formula: $A_{triangle}=\frac{1}{2}\times4\times6= 12$ square - inches.

Step3: Determine number of triangles in a pentagon

A regular pentagon can be divided into 5 congruent triangles.

Step4: Calculate area of pentagon

Multiply the area of one triangle by 5. $A_{pentagon}=5\times A_{triangle}=5\times12 = 60$ square - inches.

Answer:

C. 60 in²