Question

The diagram below shows a square inside a regular octagon. The apothem of the octagon is 13.28 units. To the nearest square unit, what is the area of the shaded region?

http://media.apexlearning.com/Images/200703/05/1683ead3-cf2b-4413-8a07-a219f502f1d0.gif

Answer 1

A = (1/2)(apothem)(perimeter)

The apothem is given in the problem statement... 13.28 units. Note in your diagram that the sides of the octagon have the same length as the sides of the squares... 11... so the perimeter of the octagon is 8 x 11 = 88. Thus, the area of the octagon, call it Ao, is:
Ao = (1/2)(apothem)(perimeter)
Ao = (1/2)(13.28)(88)
Ao = 584.32

The square's area, As, is easy to figure out.

As = 11^2 = 121

Now you can determine the area of the shaded area:

A = Ao - As
A = 584.32 - 121
A = 463.32

Answer 2

thanks i suck at math

Answer 3

My Pleasure.