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Find the area of a regular pentagon whose each side is 88 cm long and the radius of whose circumscribed circle is 77 cm.

Chapters: Area and Perimeter

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An Intiative by Sri Chaitanya

114.8 cm2

126 cm2

214 cm2

122 cm2

answer is A.

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Detailed Solution

Given, the length of each side of regular pentagon= 8 cm
The radius of circumscribed circle = 7 cm
seo

Area of pentagon

= \frac{n}{2} \times a \times \sqrt{R^{2} - \frac{a^{2}}{4}}

where n is the number of sides of the polygon, R is the radius of the circumscribed triangle and ‘a’ is the length of each side of the polygon.
Here,

n = 5, a = 8 cm and R = 7 cm

= \frac{5}{2} \times 8 \times \sqrt{7^{2} - \frac{8^{2}}{4}}

5 \times 4 \times \sqrt{49 - \frac{64}{4}}

20 \times \sqrt{49 - 16}

= 20 \sqrt{33}

cm sq.
Area of pentagon = 20×5.74
= 114.8 cm2.
Hence, Option (1) is the correct answer.

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