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Find the area of a regular decagon with a perimeter of 60 ft.

User PThomasCS
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Answer:

Area of a regular decagon with a perimeter of 60 ft. = 277 squared ft

Explanation:

Decagon has 10 sides So 60/10 = 6 (each side = 6ft )

The sum of the interior angles of a decagon is 1 440 degrees.

There are 10 equal isosceles triangles of base angles 72 degrees in a decagon

Each isosceles triangle can subdivided into 2 right-angled triangles with height h and base length = (6/2) = 3 cm and base angle 72 degrees.

Height of right-angled triangle h = 3 tan 72 ft.

Area of 1 right-angled triangle = (1/2)(3)(3 tan 72) = 13.85 squared ft

Area of decagon = 20 right-angled triangles = 277 squared ft

User Ventrilocus
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