Question 1052618: A house number is displayed on a plaque in the shape of a regular 7-sided polygon. The area of the plaque is 70 squared inches. The perpendicular distance from a side to the center is 5 inches to the nearest inch. What is the perimeter of the plaque?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The 7-sided polygon can be divided into seven triangles whose height, h is equal to the perpendicular distance from each side to the center.
The base of each triangle is equal to the length of a side, s. The area of each triangle is 1/2sh, and the area, A of the whole polygon is (1/2)h*7s,
but 7s is equal to the perimeter, P. So the formula we need is A = 1/2hP.
We are given the area and the height, so we can solve for P:
P = 2A/h = 2*70/5 = 140/5 = 28 inches.
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