Find the height of the isosceles trapezoid, the base of which is 22 cm and 10 cm, and the side is 10 cm.

An isosceles trapezoid is called, in which the sides are equal and the angles at the bases are equal.

The segment of the larger base of the trapezoid, located between its heights, is equal to the length of the smaller base:

НC = BC.

Since in this trapezoid the sides are equal, then:

AH = KD = (AD – BC) / 2;

AH = KD = (22 – 10) / 2 = 12/2 = 6 cm.

To calculate the height of the HВ, consider the triangle ΔAВH.

We apply the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BH ^ 2 + AH ^ 2;

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64;

BH = √64 = 8 cm.

Answer: the height BH is 8 cm.