In an isosceles trapezoid, the bases are 8 cm and 14 cm, the height of the trapezoid is 4 cm. find the side of the trapezoid.

Let’s draw the heights of the ВН and СK of the trapezoid Since the trapezoid is isosceles, the heights of the ВН and СK are cut off on a larger base of segments of equal length. AH = DK.
Quadrangle ВСKН is a rectangle, since ВН and СK are heights, so they are perpendicular to the bases of the trapezoid. Then НK = BC = 8 cm.
The length of the segment АН = DК = (AD – НК) / 2 = (14 – 8) / 2 = 3 cm.
In a right-angled triangle ABH, we define, by the Pythagorean theorem, the length of the hypotenuse AB.
AB^2 = BH^2 + AH^2 = 16 + 9 = 25.
AB = 5 cm.
Answer: The side of the trapezoid is 5 cm.