The diagonal of a regular quadrangular prism is √8 and is inclined to the base plane at an angle of 45

The diagonal of a regular quadrangular prism is √8 and is inclined to the base plane at an angle of 45 degrees. Find the side edge of the prism.

Since the prism is correct, there is a square at its base.

Let’s construct a diagonal AC.

The projection of the AC1 diagonal onto the base plane is the AC diagonal of the base of the prism, then the CAC1 angle is 45.

Triangle ACC1 is rectangular and isosceles, AC = CC1.

Then AC1 ^ 2 = 2 * CC1 ^ 2.

CC1 ^ 2 = AC1 ^ 2/2 = 8/2 = 4.

CC1 = 4 cm.

Answer: The length of the side edge of the prism is 4 cm.