The sides of the base of a straight rectangular parallelepiped are 4 cm and 6 cm, the side edge is 12 cm.

The sides of the base of a straight rectangular parallelepiped are 4 cm and 6 cm, the side edge is 12 cm. Find the diagonals of the parallelepiped.

We know from the condition that a rectangular parallelepiped has base side lengths of 4 and 6 cm, and the length of the side edge is 12 cm.

Let’s start solving the problem by calculating the diagonal of the base. We apply the Pythagorean theorem for this, we are looking for the unknown hypotenuse:

d = √ (a ^ 2 + b ^ 2) = √ (6 ^ 2 + 4 ^ 2) = √ (36 + 16) = √52 = 2√13 cm.

Let’s apply the formula for calculating the length of the diagonal of a parallelepiped (the same Pythagorean theorem for finding the hypotenuse):

D = √ (d ^ 2 + h ^ 2) = √ (12 ^ 2 + (√52) ^ 2) = √ (144 + 52) = √196 = 14 cm.