Find the area of the trapezoid if its height is 4, the top base is 6, the sides are 5 and √41.

univerkov | August 31, 2021 | education

From the vertices B and C we will construct the heights BK and CH. A quadrilateral BСHK is a rectangle, then KH = BC = 6 cm, and triangles ABK and CDH are rectangular.

By the Pythagorean theorem, we determine the lengths of the legs AK and DH.

AK ^ 2 = AB ^ 2 – BK ^ 2 = 25 – 16 = 9.

AK = 3 cm.

DH ^ 2 = CD ^ 2 – CH ^ 2 = 41 – 16 = 25.

DН = 5 cm.

Then AD = AK + KH + DH = 3 + 6 + 5 = 14 cm.

Determine the area of the trapezoid.

Savsd = (BC + AD) * BK / 2 = (6 + 14) * 4/2 = 40 cm2.

Answer: The area of the trapezoid is 40 cm2.

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