The height of the rectangle is 9 cm The sides of the base are 7 cm and 11 cm and one of the diagonals

The height of the rectangle is 9 cm The sides of the base are 7 cm and 11 cm and one of the diagonals of the base is 12 cm Find the diagonal of the parallelepiped.

Given:
ABCEA1B1C1E1 – straight parallelepiped,
AB = 7 centimeters,
BC = 11 centimeters,
AA1 = 9 centimeters,
AC = 12 centimeters.
Find the diagonal of the parallelepiped, that is, d -?
Solution:
Consider a straight parallelepiped ABCEA1B1C1E1. A straight parallelepiped is a parallelepiped with all its faces as rectangles. Its diagonals are equal.
Therefore, they are found by the formula:
d ^ 2 = AB ^ 2 + BC ^ 2 + AA1 ^ 2;
d ^ 2 = 7 ^ 2 + 11 ^ 2 + 9 ^ 2;
d ^ 2 = 49 + 121 + 81;
d ^ 2 = 251;
d = √251 centimeters.
Answer: √251 centimeters.