In a straight rectangular prism, the sides of the base are 13 14 15 dm, and the height is 16 cm

In a straight rectangular prism, the sides of the base are 13 14 15 dm, and the height is 16 cm, find the full surface of the prism.

By Heron’s theorem, we determine the area of the base of the prism.

The semi-perimeter of the triangle ABC is equal to: p = (AB + BC + AC) / 2 = (13 + 15 + 14) / 2 = 21 cm.

Then Sbn = √21 * (21 – 13) * (21 – 14) * (21 – 15) = √21 * 8 * 7 * 6 = √7056 = 84 cm2.

Let us determine the area of the lateral surface of the prism.

Side = Ravs * AA1, where Ravs is the perimeter of the triangle at the base of the prism.

Side = (13 + 14 + 15) * 16 = 672 cm2.

Let us determine the total surface area of the prism.

Sпов = 2 * Sсн + S side = 2 * 84 + 672 = 756 cm2.

Answer: The total surface area of the prism is 756 cm2.