# The diagonal of a regular quadrangular prism is 17, find the volume of the prism if its height is 8.

October 1, 2021 | education

| Since the prism is quadrangular and regular, there is a square at its base.

The triangle BDD1 is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg BD.

BD ^ 2 = BD1 ^ 2 – DD1 ^ 2 = 289 – 64 = 225.

ВD = 15 cm.

Diagonal BD is the hypotenuse of an isosceles right-angled triangle AED, then 2 * AB ^ 2 = BD ^ 2.

AB ^ 2 = 225/2.

AB = 25 / √2 cm.

Determine the area of the base of the prism.

Sbn = AB ^ 2 = 225/2 = 112.5 cm2.

Then V = Sosn * DD1 = 112.5 * 8 = 900 cm3.

Answer: The volume of the prism is 900 cm3.

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