In a regular quadrangular prism, the base area is 144 cm ^ 2, and the height is -14 cm.

In a regular quadrangular prism, the base area is 144 cm ^ 2, and the height is -14 cm. Determine the lengths of the diagonals of this prism.

Since the prism is correct, there are squares at its bases.

Let us define, through the area, the length of the side of the base of the prism.

Sosn = AB ^ 2 = 144.

AB = 12 cm.

We construct the diagonal AC of the square, and by the Pythagorean theorem we determine its length.

AC ^ 2 = AB ^ 2 + AD ^ 2 = 144 + 144 = 288.

AC = √288 = 12 * √2 cm.

Triangle ACC1 is rectangular, then AC1 ^ 2 = AC ^ 2 + CC1 ^ 2 = 288 + 196 = 484.

AC1 = 22 cm.

Since the diagonals of the correct prism are equal, then DB1 = AC1 = A1C = B1D = 22 cm.

Answer: The diagonals of the prism are 22 cm.