Given a trapezoid ABCD with a large base AD, AB = 6 cm, CD = 8 cm, AD = 20 cm, BC = 10 cm.

| May 2, 2021 | education

Given a trapezoid ABCD with a large base AD, AB = 6 cm, CD = 8 cm, AD = 20 cm, BC = 10 cm. Find the height of the trapezoid.

Through point C we draw a straight line CK parallel to the lateral side AB.

A quadrilateral ABCK is a parallelogram, since its opposite sides are parallel.

Then CK = AB = 6 cm, AK = BC = 10 cm.

The length of the segment is DК = АD – AK = 20 – 10 = 10 cm.

In the CDK triangle, the lengths of the sides are 6 cm, 8 cm, 10 cm, in which the Pythagorean theorem is fulfilled.

10 ^ 2 = 100.

6 ^ 2 + 8 ^ 2 = 100.

Then the triangle CDK is rectangular with right angle C.

Determine the area of the triangle CDK.

Ssdk = CK * CD / 2 = 6 * 8/2 = 24 cm2.

Also Ssdk = DK * CH / 2.

СН = 2 * Sсдк / DК = 2 * 24/10 = 48/10 = 4.8 cm.

Answer: The height of the trapezoid is 4.8 cm



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