In a rectangular trapezoid, the sides are 7cm and 25cm and the smaller base is 2cm, find the area of the trapezoid.

univerkov | September 16, 2021 | education

From the top of the trapezoid, draw the height CH. The quadrilateral ABCN is rectangular, since CH is the height, and the trapezoid ABCD is rectangular, then CH = AB = 7 cm, AH = BC = 2 cm.

In a right-angled triangle BCH, we determine the length of the leg DH.

DH ^ 2 = CD ^ 2 – CH ^ 2 = 25 ^ 2 – 7 ^ 2 = 625 – 49 = 576.

DН = 24 cm.

Then the length of the base АD = АН + DH = 2 + 24 = 26 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (2 + 26) * 7/2 = 98 cm2.

Answer: The area of the trapezoid is 98 cm2.

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