In an isosceles trapezoid, the bases are 8cm and 14cm, and the lateral side is 5cm. Find the height of the trapezoid.

Isosceles is a trapezoid in which the sides are equal:

AB = CD.

In order to calculate the length of the BH height, you need to find the length of the AH segment.

Since the segment of the larger base of the trapezoid, which is located between its heights, is equal to the length of the smaller base НК = ВС, then:

AH = KD = (AD – BC) / 2;

AH = KD = (14 – 8) / 2 = 6/2 = 3 cm.

To calculate the height of the ВН, consider the triangle AВН, which is rectangular. Let’s apply the Pythagorean theorem:

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

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16;

BH = √16 = 4 cm.

Answer: the height of the HВ is 4 cm.