A large pizza at Tony's Pizzeria is a circle with a 14-inch diameter. Its box is a rectangular prism that is 14 1/8 inches long, 14 1/8 inches wide, and 1 3/4 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. (Tip: You may use graph paper or the Virtual
Geoboard to show how your pizza can be divided into equal-sized pieces.)

To create a design for a crazy pizza that meets all of Tony's requirements, we need to go through the following steps:

1. Determine the shape and measurements of the new pizza design:
- Let's choose a irregular pentagon shape for our pizza.
- To ensure it has approximately the same area as the large pizza at Tony's Pizzeria, we can calculate the area of Tony's large pizza using the formula for the area of a circle, and then make sure the area of our pentagon is close to that value.

2. Calculate the area of Tony's large pizza:
- The diameter of the large pizza is given as 14 inches, so the radius is half of that, which is 7 inches.
- The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
- Substituting the values, we get A = π * (7 inches)^2.
- Evaluating this, we find that the area of Tony's large pizza is approximately 153.94 square inches (rounded to two decimal places).

3. Determine the measurements of the irregular pentagon:
- Irregular pentagons have different side lengths and angles, so we can choose any combination that will fit inside the box.
- Since the box dimensions are given as 14 1/8 inches long, 14 1/8 inches wide, and 1 3/4 inches tall, we need to ensure our pentagon fits within these dimensions.

4. Prove mathematically that the pentagon has approximately the same area as Tony's large pizza:
- Measure and calculate the area of the irregular pentagon using appropriate formulas for the shape to show that it is close to the area of 153.94 square inches.

5. Prove mathematically that the pentagon fits in the box:
- Measure the dimensions of the pentagon and check if they are smaller than or equal to the dimensions of the box.

6. Use diagrams or models to show that the pentagon can be divided into 8-12 equal-sized pieces:
- Use graph paper or virtual geoboards to show how lines can be drawn in the pentagon to divide it into 8-12 equal-sized sections or pieces.