Solve for a for the area of a regular polygon.

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The general formula for the area of a regular polygon is:


where the apothem is a line segment between the center and one of its sides and the perimeter is the sum of the lengths of all sides.

For a regular polygon, the apothem=`s/(2tan(180/n))`

This can be verified for an equilateral triangle (regular 3 sided polygon) where the general formula for area is:

The apothem is equal to ```s/(2tan60)=s/(2sqrt3)`

And the area is =`((3s)(s))/(2sqrt3)=(sqrt3s^2)/2`

For a square, the apothem is `s/2` and the perimeter is `4s`, therefore


For a pentagon, the apothem is = `s/(2tan36)=0.688s`

And the area is=`((0.688s)(5s))/2=1.72s^2`

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