Find the total surface area of a straight triangular prism if at the base there is a right-angled

Find the total surface area of a straight triangular prism if at the base there is a right-angled triangle with 4cm and 3cm legs and a lateral 5cm.

Let us find the area of the total surface of a straight triangular prism as the sum of the doubled area of the triangle at the base and the area of the lateral surface equal to the product of the perimeter of the triangle by the length of the lateral edge of the prism, having previously found its hypotenuse by the Pythagorean theorem.

c = √ (4 ^ 2 + 3 ^ 2) = √ (16 + 9) = √25 = 5 cm.

Sp.pov = 2Sn + Sbok.pov = 2 (1/2 * 4 * 3) + (3 + 4 + 5) * 5 = 12 + 12 * 5 = 12 + 60 = 72 cm2.

Answer: the total surface area of the prism is 72 cm2.