Mathematics: 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

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What is the area of a regular pentagon with a

Ответ:

jennnifercrd59jc

14.03.2022

Mathematics

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

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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

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