Explanation:
The shape of the new pizza must meet the conditions:
- Be an irregular polygon (different sides and/or angles).
- Have at least five sides.
- Have the approximately the same area as a 14" diameter circle.
- Fit in a 14⅛" × 14⅛" square.
- Be divisible into 8-12 equal pieces.
For simplicity, I will choose a polygon with 5 sides (a pentagon), and I will use 2 right angles (a "house" shape).
Split the pentagon into a rectangle on bottom and triangle on top. If we cut the rectangle into 8 pieces like a regular pizza, and the triangle in half, we get 10 triangles.
Now we just need to figure out the dimensions. The area of a 14" circular pizza is:
A = πr²
A = π (7 in)²
A ≈ 154 in²
That means the area of each triangle slice needs to be 15.4 in². If we make the total width of the pentagon 14", then the width of each triangle is 7", and the height of each triangle is:
A = ½ bh
15.4 in² = ½ (7 in) h
h = 4.4 in
Which makes the total height of the pentagon 3h = 13.2 in.
So, our 13.2" × 14" pentagon has at least 5 sides, is irregular, has the same area as a 14" diameter circle, fits in a 14⅛" × 14⅛" square, and can be divided into 8-12 equal pieces.
Of course, there are many possible solutions. This is just one way.