At the base of a straight prism with a side edge equal to 10, there is a rectangle with

univerkov | September 26, 2021 | education

At the base of a straight prism with a side edge equal to 10, there is a rectangle with a side of 5 and a diagonal of 13. Find the volume of the prism.

Since there is a rectangle at the base of the prism, the triangle ACD is rectangular, where, according to the Pythagorean theorem, we determine the length of the AD leg.

AD ^ 2 = AC ^ 2 – CD ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

AD = 12 cm.

Determine the area of the base of the prism.

Sbn = AB * AD = 5 * 12 = 60 cm2.

Determine the volume of the prism by the formula: Vpr = Sosn * AA1 = 60 * 10 = 600 cm3.

Answer: The volume of the prism is 600 cm3.

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