The base area of a regular quadrangular prism is 144 cm2, and the height is 12 cm. Find the diagonal of the prism.

1) At the base of a regular quadrangular prism lies a square, its area is: S = a ^ 2, which means:

a = √S = √144 = 12 (cm)

2) A regular quadrangular prism is a rectangular parallelepiped, so the square of any diagonal is equal to the sum of the squares of its three dimensions, which means:

d = √ (a ^ 2 + a ^ 2 + h ^ 2) = √ (144 + 144 + 144) = √432 = 12√3 (cm)

Answer: 12√3 cm