In a rectangular trapezoid, the bases are 22 cm and 6 cm, and the large side is 20 cm, find the smaller side.

univerkov | March 11, 2021 | education

In trapezoid ABCD, we will build the height of CH.

Since the trapezoid is rectangular, and CH is the height of the trapezoid, then the quadrangle ABCH is a rectangle, and therefore AH = BC = 6 cm.

Then DH = AD – AH = 22 – 6 = 16 cm.

The triangle CDH is rectangular, in which, according to the Pythagorean theorem, CH ^ 2 = CD ^ 2 – DH ^ 2 = 400 – 256 = 144.

CH = 12 cm.

Then AB = CH = 12 cm.

Answer: The smaller side is 12 cm.

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