Question

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?

Answer 1

No the solid is not a cube.

Explanation:

If it were a cube, the diagonal of the base would be `sqrt2` (found using the Pythagorean theorem

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

where `a` and `b` are both equal to `1` meter.

You now use a different right triangle to find the diagonal from opposite vertices, the diagonal of the base is `sqrt2`, the height is `1` (if it is a cube), and the hypotenuse is the diagonal from opposite vertices.

Again, use `a^2 + b^2 = c^2`

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

`1 + 2 != 16`