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

Answer:

The correct option is:  A.  463 square units.

Step-by-step explanation:

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

So, the perimeter$(p)$ of the octagon $=(11\times 8)units= 88\ units$

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

So, the area of the octagon:  $A=\frac{1}{2}pa=\frac{1}{2}(88)(13.28)=584.32\ units^2$

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 $=(584.32-121)units^2=463.32\ units^2 \approx 463\ units^2$