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
[tex]Area=\dfrac{1}{2}\times base\times height[/tex]
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
[tex]A_1=\dfrac{1}{2}\times \text{Side length}\times \text{Apothem}[/tex]
[tex]A_1=\dfrac{1}{2}\times 11.8\times 8.1[/tex]
[tex]A_1=47.79[/tex]
Area of five equal triangle is
[tex]A=5\times A_1[/tex]
[tex]A=5\times 47.79[/tex]
[tex]A=238.95[/tex]
So, the area of the pentagon is 238.95 square inches.
Therefore, the correct option is B.
