A formula for the surface area of a rectangular prism is
... A = 2(LW +H(L+W))
The height of the box (H) can be found by filling in the given values and solving for H.
... 1728 = 2(18·15 +H(18+15))
... 864 = 270 +33H
... (864 -270)/33 = H = 18
The height of the judges' box is 18 inches, so the 17.75-inch robot meets the height requirement.