Question

A new refrigerator comes packaged in a box shaped like a rectangular prism. The base of the box measures 6 feet by 12 feet. The total surface area of the box is 396 square feet. What is the height of the box in feet?​

Answer 1

7 feet

Explanation:

You want the height of a 6' by 12' cuboid box that has a total surface area of 396 square feet.

Surface area

The formula for the surface area of a cuboid is ...

SA = 2(LW +H(L+W))

Application

For the given box, this is ...

396 = 2(6·12 +H(6+12))

198 = 72 +18H . . . . . . . . . . divide by 2

126 = 18H . . . . . . . . . . . subtract 72

7 = H . . . . . . . . . . . . divide by 18

The height of the box is 7 feet.