Answer
169 square inches
Work Step by Step
Volume of a box is $length * width * height$.
We know that the height is $4$ inches and the total volume is 100 cubic inches.
Shape of the box does not matter our volume just has to equal 100. So let's use this formula to solve:
$x*x*4 = 100$
$4x^2 = 100$
$x^2 = 25$
$x = \sqrt 25$
$x = 5$
Now we know that the base of the box is 5 inches wide by 5 inches long but since we need a piece of cardboard to fold up to give it the sides we need to include the 4 inches for each side on top of the length/width. So we have:
$5+4+4 = 13$ per side.
and $13 * 13 = 169$ square inches
