Question

What is the area of a regular pentagon with a side length of 10 inches and a distance from the center to a vertex of 10 inches? Round your answer to the nearest tenth.

A. 96.3 in^2
B. 172.0 in.^2
C. 344.1 in.^2
D. 192.6 in.^2

Answer 1

The correct option is B. 172 square inches

Explanation:

Side length of the regular pentagon = 10 inches

Area of the regular pentagon is given by :

`Area = (1)/(4)(\sqrt{25+10√(5)})\cdot side^2\\\\\implies Area = (1)/(4)(\sqrt{25+10√(5)})\cdot 10^2\\\\\implies Area = (1)/(4)(\sqrt{25+10√(5)}) \cdot 100\\\\\implies Area =25* (\sqrt{25+10√(5)})\\\\\implies Area = 172.04 \:\:inches^2\\\\\bf\implies Area\approx 172 \:\:inches^2`

Hence, the correct option is B. 172 square inches