Question 766552
A regular pentagon has sides of 20 cm. an inner pentagon with sides of 10 cm is inside and concentric to the larger pentagon. What is the area inside the larger pentagon and outside the smaller pentagon?
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For a regular polygon with n sides of length s:
{{{Area = ns^2*cot(180/n)/4}}}
For s = 20:
{{{Area = 5*400*cot(36)/4 = 500*cot(36)}}}
The area of the 10 cm = 1/4 of the 20 = {{{125*cot(36)}}}
Area between = 375*cot(36)
=~ 516.143 sq cm