Find the total surface area of a straight triangular prism if its height is 5cm, and the lengths

Find the total surface area of a straight triangular prism if its height is 5cm, and the lengths of the sides of the base are 40cm, 13cm, 37cm.

Since the prism is rectangular, its side faces are rectangles.

Let’s define the perimeter of the triangle ABC.

Ravs = AB + BC + AC = 40 + 13 + 37 = 90 cm.

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

S side = P * AA1 = 90 * 5 = 450 cm2.

The area of the base of the prism is determined by Heron’s theorem, for which we define the semiperimeter of the triangle ABC. p = P / 2 = 90/2 = 45 cm.

Then Sbn = √45 * (45 – 40) * (45 – 37) * (45 – 13) = √45 * 5 * 8 * 32 = √57600 = 240 cm2.

Then Sпов = Sbok + 2 * Sсн = 450 + 480 = 930 cm2.

Answer: The surface area of the prism is 930 cm2.