A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. What is the approximate area of the heptagon rounded to the nearest whole number? Recall that a heptagon is a polygon with 7 sides.

Question

Mathematics

Mercado

14 April, 05:25

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. What is the approximate area of the heptagon rounded to the nearest whole number? Recall that a heptagon is a polygon with 7 sides.

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Answers (2)

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Lucy Dawson · Answer 1

2,125 cm^2 on edgenu

Adalynn Acosta · Answer 2

If you know the side length, you don't need the radius to calculate the area. The area for any regular polygon is:

A (n, s) = (ns^2) / (4tan (180/n)), where n=number of sides and s=length of sides.

The above is derived by dividing the polygon into n triangles ... anyway, in this case:

A = (7 * 24.18^2) / (4tan (180/7)

A = 1023.1767/tan (180/7)

A=2124.65 cm^2 (to nearest one-hundredth)