In a straight triangular prism with a base of a right-angled triangle with a leg of 8dm and an area of 24dm2

In a straight triangular prism with a base of a right-angled triangle with a leg of 8dm and an area of 24dm2, the height of the prism is 9 dm. Find the surface area of the prism.

Knowing the leg and the area of the right-angled triangle, we determine the length of the second leg.

Sosn = АС * ВС / 2.

АС = 2 * Sсн / ВС = 2 * 24/8 = 6 cm.

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

AB ^ 2 = BC ^ 2 + AC ^ 2 = 64 + 36 = 100.

AB = 10 dm

Let’s define the perimeter of the triangle ABC.

Rosn = AB + BC + AC = 10 + 8 + 6 = 24 dm.

Let’s calculate the area of the lateral surface of the prism.

Sside = Rosn * BB1 = 24 * 9 = 216 dm2.

Then Sпов = 2 * Sсн + Sbok = 2 * 24 + 216 = 264 dm2.

Answer: The surface area of the prism is 264 dm2.