Given a regular quadrangular prism, the side of the base is 12 cm, the side edge is 14 cm.

Given a regular quadrangular prism, the side of the base is 12 cm, the side edge is 14 cm. Calculate the length of the diagonal of the prism.

Since the prism is correct, there is a square at its base, and the side faces are equal rectangles.

Construct the diagonal BD of the square ABCD.

By the Pythagorean theorem, BD ^ 2 = AB ^ 2 + AD ^ 2 = 144 + 144 = 288.

ВD = 12 * √2 cm.

Diagonal DВ1 is the hypotenuse of the right-angled triangle ВDВ1, then, by the Pythagorean theorem:

DB1 ^ 2 = BD ^ 2 * BB1 ^ 2 = 288 + 196 = 484.

DB1 = 22 cm.

Answer: The diagonal of the prism is 22 cm.