The lateral edge of a straight triangular prism is 9 cm long. Find the total surface area

The lateral edge of a straight triangular prism is 9 cm long. Find the total surface area of the prism if its base is a right-angled triangle, the legs of which are 3 cm and 4 cm.

At the base of the prism there is a right-angled triangle ABC with an angle B = 90.

Let us define, according to the Pythagorean theorem, the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 4 ^ 2 + 3 ^ 2 = 16 + 9 = 25.

AC = 5 cm.

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

Side = AA1 * (AB + BC + AC) = 9 * (4 + 3 + 5) = 9 * 12 = 108 cm2.

Find the area of the base of the prism.

Sb = (AB * BC) / 2 = 4 * 3/2 = 6 cm2.

Determine the total surface area of the prism.

Stot = Sside + 2 * Sb = 108 + 2 * 6 = 120 cm2.

Answer: The total surface area of the prism is 120 cm2.