# A clear plastic prism has six faces, each of which is a parallelogram of side length 1 meter. A diagonal made of nylon filament line connecting two opposite vertices of the solid has a length of 4 meters. ls the solid a cube?

##### 1 Answer

No the solid is not a cube.

#### Explanation:

If it were a cube, the diagonal of the base would be

#a^2 + b^2 = c^2# ,

where

You now use a different right triangle to find the diagonal from opposite vertices, the diagonal of the base is

Again, use

#1^2 + (sqrt2)^2 = 4^2#

#1 + 2 != 16#