The larger base of the isosceles trapezoid is 34 cm, the smaller base is 18 cm, and the lateral side

The larger base of the isosceles trapezoid is 34 cm, the smaller base is 18 cm, and the lateral side is 17 cm, calculate the height of the trapezoid.

A trapezoid is a quadrilateral in which one pair of opposite sides is parallel, and the sides are not equal to each other.

Equilateral is a trapezoid in which the sides are equal.

Since the segment of the larger base located between the heights is equal to the length of the smaller base, then:

NC = BC.

Since the trapezoid is isosceles, then:

AH = KD.

In this way:

AH = KD = (AD – BC) / 2;

AH = KD = (34 – 18) / 2 = 16/2 = 8 cm.

To calculate the height BH, consider the triangle ΔABH. To calculate BH, 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 = 17 ^ 2 – 8 ^ 2 = 289 – 64 = 225;

BH = √225 = 15 cm.

Answer: HV height is 15 cm.