The base of a straight triangular prism is a rectangular triangle with legs 9 and 40

The base of a straight triangular prism is a rectangular triangle with legs 9 and 40, the lateral edge of the prism is 50. Find the area of the lateral surface of the prism.

The lateral surface of a rectangular prism, at the base of which a right-angled triangle lies, will consist of rectangles with sides 1) a lateral rib and the first leg of the base triangle; 2) the lateral rib and the second leg of the base triangle; 3) lateral rib and hypotenuse of the base triangle. We do not know the hypotenuse of the base of the prism, we will find it by the Pythagorean theorem.

Let us denote the hypotenuse of the base of the prism c, the legs of the base of the prism a = 9, b = 40, the lateral edge of the prism h = 50.

c ^ 2 = a ^ 2 + b ^ 2;

c ^ 2 = 9 ^ 2 + 40 ^ 2 = 81 + 1600 = 1681; c = 41.

S = S1 + S2 + S3;

S1 = ah; S2 = bh; S3 = ch;

S = ah + bh + ch = h (a + b + c);

S = 50 (9 + 40 + 41) = 50 * 90 = 4500.

Answer. 4500.