In trapezoid ABCD, the sides AB and CD are equal, CH is the height drawn to the larger base of AD.

| March 19, 2021 | education

In trapezoid ABCD, the sides AB and CD are equal, CH is the height drawn to the larger base of AD. Find the length of the line segment HD if the middle line KM of the trapezoid is 12 and the smaller base BC is 4.

Since in this trapezoid the sides AB and CD are equal, this trapezoid is isosceles, which means that the segments AN and HD will also be equal.

Since the length of the midline of the trapezoid is equal to the half-sum of its bases, then to calculate the larger of them you need:

KM = (BC + AD) / 2;

(BC + AD) = 2 KM;

AD = 2 KM – BC;

AD = 2 12 – 4 = 24 – 4 = 20 cm.

Since the length of the smaller base BC is equal to the segment ND, which is part of the larger base AD and is located between the heights BN and CH, then:

HD = AN = (AD – NH) / 2;

НD = AN = (20 – 4) / 2 = 16/2 = 8 cm.

Answer: the length of the segment НD is 8 cm.



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