Question

Find the area of a regular pentagon with an apothem of 6 inches and a side length of 8.7 inches. Round to the nearest tenth.

Answer 1

1. The area of the pentagon is 130.5 inches. The area of a pentagon, if you don’t know, is equal to the perimeter of the pentagon times the apothem, all divided by 2. Because one side of the pentagon has a length of 8.7 inches, and all sides of a pentagon have the same length, then the perimeter would be equivalent to 8.7 times 5, which equals a perimeter of 43.5 inches. Now that our perimeter is found, our equation is set (because the apothem is 6 inches, as said in the problem). Now, to solve, we have to multiply the perimeter (43.5 in.) by the apothem (6 in.), which equals 261 inches. Now, all we have to do is divide it by 2, which will give us our answer of 130.5 inches. Bonus: The answer only reaches out to one decimal point, meaning that there is no need to round!