Question

1.

(05.03)

Calculate the area of the regular pentagon below:
A regular pentagon with a side length of 11.8 inches and a dotted line from center to middle of side of 8.1 inches.

(4 points)
164.025 square inches
238.95 square inches
351.78 square inches
477.9 square inches

Answer 1

Given:

A regular pentagon with a side length of 11.8 inches and a dotted line from center to middle of side of 8.1 inches.

To find:

The area of the regular polygon.

Solution:

We have,

Side length = 11.8 inches

Length of Apothem = 8.1 inches

Area of a triangle is

`Area=(1)/(2)* base* height`

A regular pentagon has 5 equal sides and equal interior angles. The lines from the center to the vertices divide the pentagon in 5 equal triangle.

Area of one triangle is

`A_1=(1)/(2)* \text{Side length}* \text{Apothem}`

`A_1=(1)/(2)* 11.8* 8.1`

`A_1=47.79`

Area of five equal triangle is

`A=5* A_1`

`A=5* 47.79`

`A=238.95`

So, the area of the pentagon is 238.95 square inches.

Therefore, the correct option is B.