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What is the area of a 7 sided polygon with an apothem of 2.5 and s radius of 2.77?

 Apr 22, 2016
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A regular 7-sided polygon can be thought of as being made of 7 isosceles triangles.  Each triangle has an apex angle theta = 2pi/7.  The height is h = 2.5 and half the base length is b = h*tan(theta/2).  Hence the overall area of the polygon is:

 

A = 7*b*h   or  A = 7*2.5*tan(pi/7)*2.5  or  A ≈ 21.07

 Apr 23, 2016

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