Find the volume and height of a regular quadrangular prism, with base sides 2 cm and

Find the volume and height of a regular quadrangular prism, with base sides 2 cm and a diagonal drawn to the plane at an angle of 45 °

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

The diagonal AC divides the square ABCD into two right-angled isosceles triangles. Angle CAD = ACD = 45.

Then AC = AD / SinACD = 2 / (√2 / 2) = 4 / √2 = 2 * √2 cm.

Triangle AA1C is rectangular and isosceles, since the angle ACA1 = 45, then AA1 = AC = 2 * √2 cm.

Let’s define the volume of the prism.

V = Sbase * АА1 = AB * АD * АА1 = 2 * 2 * 2 * √2 = 8 * √2 cm3.

Answer: The volume of the prism is 8 * √2 cm3, the height of the prism is 2 * √2 cm.