A pizzeria makes pizzas in the shape of a regular octagon, and cuts them into 8 identical triangular slices. The diameter of the pizza is 12 inches.

Subject- Math

Question-A pizzeria makes pizzas in the shape of a regular octagon, and cuts them into 8 identical triangular slices. The diameter of the pizza is 12 inches.

Answer- 172.8 square inches, certainly large enough for the pizza..

Explanation- A hexagon is a good choice for a problem like this.

If you draw a regular hexagon, you will see that the distance across it must be the same 14 1/8" to clear the 14" pizza...that distance must be side to side not vertex to vertex...

That 14 1/8" distance is the length of two apothems.

Thus the apothem is 7 1/16".

We can find the side of the hexagonal box by realizing that a hexagon is really just six equilateral triangles in one figure.

We have to multiply the apothem by 2/√3

We get

Side length = 7.0625·(2/√3)=8.155 inches

The area of said hexagon would be

A=(1/2)·ap=(1/2)*(7.0625)*(6*8.155)=

172.8 square inches