The base of a straight triangular prism is a right-angled triangle with legs 5 and 12

The base of a straight triangular prism is a right-angled triangle with legs 5 and 12, the lateral edge of the prism is 8. Find the area of the lateral surface of the prism.

In order to find the area of the lateral surface of a prism, we need to know the length of all sides of its base.

The base of this is a right-angled triangle, the legs of which are known to us. So the third side, we denote it by the letter x, is the hypotenuse of this triangle and to find it we use the Pythagorean theorem:

x² = 12² + 5²,

x² = 169,

x = 13.

Now we can find the lateral surface area of this prism:

S = 12 * 8 + 5 * 8 + 13 * 8 = 8 * (12 + 5 + 13) = 8 * 30 = 24 cm².