We want to find the area of a regular octagon with an apothem that measures 18.5cm and a side length of 15cm. Recall that a regular octagon is a regular polygon with 8 congruent sides.
The area of a regular polygon is half the product of the apothem and the perimeter. We are given the apothem but are missing the perimeter. Since all 8 sides are congruent, to find the perimeter we will multiply the side length 15 by 8.
15* 8=120cm
We know that the apothem is 18.5cm and we found that the perimeter is 120cm. To find the area of the polygon we will substitute these values in the formula A= 12ap, then simplify.
