Alarge pizza at tony's pizzeria is a circle with a 14-inch diameter. its box is a rectangular prism that is 1 14 8 inches long, 1 14 8 inches wide, and 3 1 4 inches tall. your job is to design a crazy new shape for a large pizza. it can be any irregular polygon shape, but it must have at least five sides.

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".