Find the area of a rectangular trapezoid in which the bases are 22cm and 6cm and the large side is 20cm.

univerkov | May 2, 2021 | education

1. The tops of the trapezoid – A, B, C, D. ∠A = ∠B = 90 °. ВС = 6 cm. АD = 22 cm. СD = 20 cm. СН – height. S is the area of the trapezoid.

2. BC = AH, since in the rectangle ABCH the opposite sides are equal.

3. Segment DH = AD – AH = 22 – 6 = 16 cm.

4. Calculate the length of the CH height using the Pythagorean theorem:

CH = √СD² – DH² = √20² -16² √400 – 256 = √144 = 12cm.

5. S = (AD + BC) / 2 x CH = (22 + 6) / 2 x 12 = 168 cm².

Answer: S is equal to 168 cm².

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