At the base of a straight prism there is a right-angled triangle with legs 12 cm

univerkov | May 17, 2021 | education

At the base of a straight prism there is a right-angled triangle with legs 12 cm and 15 cm, find the height of the prism if the surface area of the prism is 864 cm?

At the base of the prism lies a right-angled triangle ABC, then according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 15 ^ 2 + 12 ^ 2 = 225 + 144 = 369.

AC = 3 * √41 cm.

The area of the lateral surface of the prism is: Sside = P * AA1, where P is the perimeter of the triangle at the base of the prism.

P = 12 + 15 + 3 * √41 = 27 + 3 * √41 cm.

864 = (27 + 3 * √41) * AA1.

AA1 = 864 / (27 + 3 * √41) = 864 / 46.21 = 18.7 cm.

Answer: The height of the prism is 18.7 cm.

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