SOLUTION: Find the perimeter in inches of a regular polygon whose area is 24 square root 3 inches, and whose apothem, the perpendicular distance from the center of the regular polygon to one

Question 1060916: Find the perimeter in inches of a regular polygon whose area is 24 square root 3 inches, and whose apothem, the perpendicular distance from the center of the regular polygon to one of its sides, is 2 square root 3 inches.
Answer by ikleyn(52807) (Show Source): You can put this solution on YOUR website!
.
Find the perimeter in inches of a regular polygon whose area is 24 square root 3 inches, and whose apothem,
the perpendicular distance from the center of the regular polygon to one of its sides, is 2 square root 3 inches.
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The area of this regular polygon (of every regular polygon, actually) is half of the product of its perimeter by the apothem:


A = .   (1)


You easily can get (can prove) this formula by drawing the segments from the center of the polygon to all its vertices. 
The segments divide the polygon into the union of congruent triangles. By applying the formula for the area of every single triangle, 
you sum up their areas to the right side of the formula (1).


Now, from (1) you have P =  =  = 24 inches.


Answer.  The perimeter = 24 inches.

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