The base of the right-angled prism is a right-angled triangle with 3 and 4 cm legs.

The base of the right-angled prism is a right-angled triangle with 3 and 4 cm legs. The total surface area of the prism is 120 cm2. Find the volume of the prism.

By the Pythagorean theorem, we find the hypotenuse of the right-angled triangle lying at the base of this prism:

c ^ 2 = 3 ^ 2 + 4 ^ 2 = 9 + 16 = 25 = 52;

c = 5 cm – base hypotenuse.

The base area is equal to half the product of the legs:

Sb = 0.5 * 3 * 4 = 6 cm2.

The lateral surface area is equal to the difference between the areas of the full surface and the two bases:

Sside = Sful – 2 * Sbn = 120 – 2 * 6 = 120 – 12 = 108 cm2.

On the other hand, the lateral surface area is equal to the product of the height of the prism and the perimeter of the base:

Sside = h * P = h * (3 + 4 + 5) = h * 12;

h = S side / 12 = 108/12 = 9 cm.

The volume of the prism is equal to the product of the height and the area of ​​the base:

V = Sbn * h = 6 * 9 = 54 cm3.