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?

Answer 1

463 square units. ok

Answer 2

The correct option is: A. 463 square units.

Explanation:

According to the given diagram, the side length of the regular octagon is 11 units.

So, the perimeter
`(p)` of the octagon
`=(11* 8)units= 88\ units`

The apothem
`(a)` of the octagon is 13.28 units.

So, the area of the octagon:
`A=(1)/(2)pa=(1)/(2)(88)(13.28)=584.32\ units^2`

Now, the side length of the inside square is 11 units. So, the area of the square
`=(11)^2 =121\ units^2`

Thus, the area of the shaded region
`=(584.32-121)units^2=463.32\ units^2 \approx 463\ units^2`