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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