# At the base of the straight prism lies a right-angled triangle of the legs, which are equal

May 27, 2021 | education

| **At the base of the straight prism lies a right-angled triangle of the legs, which are equal to 40 cm and 9 cm, and the height is 10. Find the surface area.**

Knowing the lengths of the legs of a right-angled triangle at the base of the prism, we determine its area.

Sosn = BC * AC / 2 = 9 * 40/2 = 180 cm2.

By the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = BC ^ 2 + AC ^ 2 = 81 + 1600 = 1681.

AB = 41 cm.

The lateral surface area is equal to: Sbok = AA1 * P, where P is the perimeter of the ABC triangle.

Side = 10 * (9 + 40 + 41) = 900 cm2.

Let us determine the total surface area of the prism.

Spov = 2 * Sb + S side = 2 * 180 + 900 = 1260 cm2.

Answer: The surface area is 1260 cm2.

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