The Box has perimeter of 48 inches which is a square.
Perimeter of square is side * side.
![perimeter = side * side](https://tex.z-dn.net/?f=%20perimeter%20%3D%20side%20%2A%20side%20)
plugging value of perimeter here to get side
![48 = 4 * side](https://tex.z-dn.net/?f=%2048%20%3D%204%20%2A%20side%20)
![side = 48/4](https://tex.z-dn.net/?f=%20side%20%3D%2048%2F4%20%20)
side =12 inches.
Area of square box = side *side = 12*12 =144 in².................(1)
Now we are given circumference of pizza as 37.68 inches.
Circumference of circle is given by:
![c=2\pi r](https://tex.z-dn.net/?f=%20c%3D2%5Cpi%20r%20)
![37.68=2\pi r](https://tex.z-dn.net/?f=%2037.68%3D2%5Cpi%20r%20)
finding r from here we have
r=6 inches.
Area of circle is given by :
![A = \pi r^{2}](https://tex.z-dn.net/?f=%20A%20%3D%20%5Cpi%20r%5E%7B2%7D%20%20)
plugging value of r,
![A = \pi 6^{2}](https://tex.z-dn.net/?f=%20A%20%3D%20%5Cpi%206%5E%7B2%7D%20%20)
Area of pizza = 113.04 in²...................(2)
Difference = (1) -(2) = 144 - 113.04 = 30.96 in²
the difference in the area of the pizza and the area of the pizza box is approximately 31 inches square.