At the base of the straight prism lies a right-angled triangle with a 4 cm leg

At the base of the straight prism lies a right-angled triangle with a 4 cm leg and a 5 cm hypotenuse. The side surface area is 120 cm2. Find the volume of the prism.

Triangle ABC is rectangular by condition, then, by the Pythagorean theorem, BC ^ 2 = AB ^ 2 – AC ^ 2 = 25 – 16 = 9.

BC = 3 cm.

Let’s define the perimeter of the triangle ABC. Ravs = (AB + BC + AC) = 5 + 3 + 4 = 12 cm.

Savs = Sosn = AC * BC / 2 = 4 * 3/2 = 6 cm2.

The area of the lateral surface of the prism is: Sbok = Rosn * CC1.

CC1 = Sside / Rosn = 120/12 = 10 cm.

Then the volume of the prism is:

Vpr = Sbn * CC1 = 6 * 10 = 60 cm3.

Answer: The volume of the prism is 60 cm3.