SOLUTION: A stop sign is a regular octogon. Each side of the sign is 12.6 in long. The area of the stop sign is 770 in squared. What is the length of the apothem to the nearest whole number.

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Question 593322: A stop sign is a regular octogon. Each side of the sign is 12.6 in long. The area of the stop sign is 770 in squared. What is the length of the apothem to the nearest whole number. Show Your Work.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Here is the regular octagon with one apothem drawn in red:



Area = (apothem)(perimeter) 

The area is given as 770 inē.

The perimeter is 8 times 12.6 in or 100.8 in.

Replacing "Area" by 770, perimeter by 100.8 in

Area = (apothem)(perimeter)

 770 = (apothem)(100.8)

Multiply the  by the 100.8 getting 50.4

 770 = 50.4(apothem)

Divide both sides by 50.4:

  = apothem

    15.27777778 = apothem

To the nearest whole number 15 inches.

Edwin
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