A large 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.
Tony says he will make and sell your crazy pizza if you can prove the following:
• It is approximately the same area as the large pizza he sells now.
• It fits inside the large box listed above.
• It can be cut into 8‒12 equal-sized pieces.
Create one design for a crazy pizza that will meet all of Tony's requirements.
1. Create a representation of your design that includes measurements.
2. Prove mathematically, using appropriate formulas, that your design is
approximately the same surface area as Tony’s large pizza.
3. Prove mathematically, using appropriate formulas, that your pizza will fit in
the box.
4. Use diagrams or other models to prove that your design can be divided into
8‒12 equal-sized pieces.
23 answers
Consider using a regular pentagon with an apothem of 7", or the radius of the pizza. Look online to find the area of such a figure. It will be the smallest 5-sided box that will hold the pizza.
ANY figure can be divided into 8-12 pieces of equal size. Depending on how crazy it is, they might not be suitable to fit a pizza slice. (Of course, the pizza slices don't have to be the usual shape, either!)
pentagon area
Then try something simple like a pentagon (3 triangles of equal size). If you take the area of the pizza and divide it into 3, you will get the area of each triangle. From there you need to determine the size of your triangles using the formula for area of a triangle.
I hope that at least gets you going in the right direction....