The base of a straight triangular prism is a right-angled triangle with legs 6 and 8, its surface is 288

The base of a straight triangular prism is a right-angled triangle with legs 6 and 8, its surface is 288 Find the height of the prism

Knowing the legs of a right-angled triangle, according to the Pythagorean theorem, we can find its hypotenuse:

c ^ 2 = a ^ 2 + b ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 +64 = 100 = 102;

c = 10 – hypotenuse.

We find the area of the base as half of the product of the legs:

Sb = 0.5 * a * b = 0.5 * 6 * 8 = 24.

The total surface area of the prism is equal to the sum of the areas of the lateral surface and the two bases:

S full = S side + 2 * S main.

Hence:

S side = S full – 2 * S main = 288 – 2 * 24 = 288 – 48 = 240.

The lateral surface area is equal to the product of the perimeter of the base and the height of the prism.

Sside = P * h;

h = Sside / P = 240 / (6 + 8 + 10) = 240/24 = 10 – the height of this prism.