The base of a straight prism is a right-angled triangle with a leg of 3 cm and a hypotenuse of 2√5

univerkov | April 29, 2021 | education

The base of a straight prism is a right-angled triangle with a leg of 3 cm and a hypotenuse of 2√5 cm, the lateral edge is 4 cm. Find the volume of the prism.

The volume of the prism is equal to the product of the area of the base of the prism and the height. V = S main. * h. The height of the straight prism is equal to the lateral rib.

Find the area of the base of the prism. At the base is a right-angled triangle. Its area is equal to half the product of its legs. We know the hypotenuse and leg, we will find the second leg according to the Pythagorean theorem.

x ^ 2 = (2√5) ^ 2 – 3 ^ 2 = 4 * 5 – 9 = 20 – 9 = 11; x = √11 (cm).

S main. = 1/2 * 3 * √11 = 1.5 √11 (cm ^ 2).

V = 1.5 √11 * 4 = 6 √11 (cm ^ 3).

Answer. 6 √11 cm ^ 3.

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