# The base of a straight prism is a right-angled triangle with 4 and 3 cm legs. The diagonal of the side face containing

August 31, 2021 | education

| **The base of a straight prism is a right-angled triangle with 4 and 3 cm legs. The diagonal of the side face containing the hypotenuse of the triangle is 13 cm. Calculate the side surface of the prism.**

Let us determine the length of the hypotenuse AB in the base of the prism.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 16 + 9 = 25.

AB = 5 cm.

Since, by condition, the prism is straight, the triangle AB1B is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg BB1.

BB1 ^ 2 = AB1 ^ 2 – AB ^ 2 = 169 – 25 = 144.

BB1 = 12 cm.

Determine the perimeter of the base of the prism.

Rosn = AC + BC + AB = 4 + 3 + 5 = 12 cm.

Then Sbok = Rosn * BB1 = 12 * 12 = 144 cm2.

Answer: The area of the lateral surface of the prism is 144 cm2.

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