SOLUTION: The perimeter of a regular polygon is 48 and its apothem is 6.What is the area of the polygon?

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Question 745052: The perimeter of a regular polygon is 48 and its apothem is 6.What is the area of the polygon?
Answer by savvyhush23(50) About Me  (Show Source):
You can put this solution on YOUR website!
I hope you know what is the apothem of a regular polygon. If not just google it.
Ok, let us inscribed a circle in a regular polygon so that its radius is equal to the apothem.
The formula of Regular polygon Circumscribing a circle are:
Perimeter+=+2nr+tan%28180%2Fn%29 and Area+=+nr%5E2tan%28180%2Fn%29
In the perimeter formula, see that tan%28180%2Fn%29=+Perimeter%2F2nr, substitute it to the Area:
Area+=+nr%5E2%28P%2F2nr%29+=+r%2848%2F2%29 where r = 6
Therefore, Area = 144 sq. unit.