At the base of a straight prism lies an isosceles rectangular triangle with a hypotenuse of 4√2

At the base of a straight prism lies an isosceles rectangular triangle with a hypotenuse of 4√2, the height of the prism is 5, find the volume of the prism.

Since at the base of the prism lies a right-angled isosceles triangle, AC = BC, and then, by the Pythagorean theorem, 2 * AC ^ 2 = AB ^ 2 = (4 * √2) ^ 2 = 32.

AC ^ 2 = 32/2 = 16.

AC = 4 cm.

Then the area of the base of the prism is equal to: Sbn = AC ^ 2 = 16 cm2.

The volume of the pyramid will be equal to: Vpr = Sosn * AA1 = 16 * 5 = 90 cm3.

Answer: The volume of the prism is 90 cm3.