In a straight Triangular prism, the sides of the base are 36; 29; 25, and the total surface

In a straight Triangular prism, the sides of the base are 36; 29; 25, and the total surface contains 1620. Determine the height of the prism.

The perimeter of the ABC triangle will be equal to: Ravs = (25 + 29 + 36) = 90 cm.

Then the half-perimeter is equal to: p = P / 2 = 45.

Let us determine the area of the base by Heron’s theorem.

Sb = √45 * (45 – 25) * (45 – 29) * (45 – 36) = √45 * 20 * 16 * 9 = √129600 = 360 cm2.

S floor = 2 * S main + S side.

Sside = S floor – 2 * Sb = 1620 – 2 * 360 = 900 cm2.

Sside = P * CC1.

900 = 90 * CC1

CC1 = 900/90 = 10 cm.

Answer: The height of the prism is 10 cm.