Question

Find the area of the regular polygon. Give the answer to the nearest tenth.

Answer 1

A regular dodecagon is a polygon with 12 equal sides.
Length of each side = 108/12 = 9 cm.

Length of the apothem = (9/2)/tan 15 = 9/2tan 15 = 16.79 cm

Area of each triangle = 9/2(16.79) = 75.57 cm^2

Therefore, area of the dodecagon = 12(75.57) = 906.9 cm^2

Answer 2

Each side is 9 cm long 


a 12 sided regular polygon is composed of 24 right triangles with one side

half the length of a side = 4.5 cm 

the other side is 4.5 / tan (360/24) = 4.5 / tan(15) 


A = 24 (1/2) 4.5^2 / tan(15) = 906.9 cm^2 


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