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

Answer:  

The correct option is B. 172 square inches

Step-by-step explanation:

Side length of the regular pentagon = 10 inches

Area of the regular pentagon is given by :

$Area = \frac{1}{4}(\sqrt{25+10\sqrt{5}})\cdot side^2\\\\\implies Area = \frac{1}{4}(\sqrt{25+10\sqrt{5}})\cdot 10^2\\\\\implies Area = \frac{1}{4}(\sqrt{25+10\sqrt{5}}) \cdot 100\\\\\implies Area =25\times (\sqrt{25+10\sqrt{5}})\\\\\implies Area = 172.04 \:\:inches^2\\\\\bf\implies Area\approx 172 \:\:inches^2$

Hence, the correct option is B. 172 square inches