The bases of the trapezoid are 5 and 17, and its sides are 10. Find the area of the trapezoid.

Based on the fact that the sides of the trapezoid are equal, then we have an isosceles trapezoid. Formula for the area of an isosceles trapezoid:
S = (a + b / 2) * √c ^ 2- (a-b) ^ 2/4, where a is the larger base of the trapezoid, b is the smaller base of the trapezoid, c is the side. Knowing that c = 10 cm, b = 5 cm, c = 17 cm, we calculate the area of the trapezoid.
S = 17 + 5/2 * √17 ^ 2- (17-5) ^ 2/4 = 11 * √ 289 – 144/4 = 11 * √289-36 = 11 * √325 = 11 * √25 * 13 = 11 * 5√13 = 55√13 cm ^ 2.
Answer: 55√13 cm ^ 2.