In an isosceles trapezoid, the base 43 and 33, the height is 12, find the side of the trapezoid.

Let’s draw the height of CM. In a rectangle KBCM, KM = BC = 33 – as opposite sides of the rectangle. Hence AK = MD = (AD – KM) / 2 = (43 – 33) / 2 = 5.

From the obtained right-angled triangle ABK, we find the hypotenuse AB by the Pythagorean theorem

(the square of the hypotenuse is equal to the sum of the squares of the legs): AB ^ 2 = BK ^ 2 + AK ^ 2 = 12 ^ 2 + 5 ^ 2 = 144 + 25 = 169. AB = √169 = 13. AB is the side of the trapezoid.

Answer: 13.