In the image ( see below), the figure represents a single sheet of cardboard.
It can be folded along the dotted lines into a rectangular box with square sides, a longest side of 12 inches, and volume of 300 cubic inches.
If the piece was cut from a square sheet of cardboard, what is the minimum required area of the sheet of cardboard (in square inches)?
Note the figure is not drawn to scale.
Since the sides are square those flaps, and the width of all the segments, must be 5.
That checks with the volume = 5 * 5 * 12 = 300.
Then the width of the cut out is 12 + 5 + 5 = 22.
The length (height) is 20.
The minimum sides for that square are 22 x 22, for an area of 484.
Checking if that is correct.