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mario62 [17]
2 years ago
6

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

Mathematics
1 answer:
Naddik [55]2 years ago
5 0

Answer:

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

Step-by-step 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

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