At the base of a straight prism lies a right-angled triangle with a leg of 4m and a hypotenuse of 5m

| May 6, 2021 | education

At the base of a straight prism lies a right-angled triangle with a leg of 4m and a hypotenuse of 5m, and a diagonal of a smaller side facet of 13 m. Find the area of the lateral surface of the prism.

Since at the base of the prism there is a right-angled triangle, then, according to the Pythagorean theorem, we determine the length of the leg AB.

BC ^ 2 = AC ^ 2 – BC ^ 2 = 5 ^ 2 – 4 ^ 2 = 25 – 16 = 9.

BC = 3 cm.

In the side face of BB1C1C, the triangle BB1C is rectangular, then, according to the Pythagorean theorem, we determine the length of the leg BB1.

BB1 ^ 2 = CB1 ^ 2 – BC ^ 2 = 13 ^ 2 – 3 ^ 2 = 169 – 9 = 160 = 4 * √10 cm.

Let us determine the area of the lateral surface of the prism.

Sside = P * BB1, where P is the perimeter of the triangle at the base of the prism.

Side = (4 + 3 + 5) * 4 * √10 = 48 * √10 cm2.

Answer: The total surface area of the prism is 48 * √10 cm2.



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