# The base of the trapezoid is 5.1 dm and 6.9 dm, the side is 41 cm. Find the area of the trapezoid.

August 17, 2021 | education

| AB = CD = 41 cm = 4.1 dm.

We construct the height BH, which divided the larger base AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases of the trapezoid.

AH = (AD – BC) / 2 = (6.9 – 5.1) / 2 = 0.9 dm.

In a right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the leg AH.

AH ^ 2 = AB ^ 2 – BH ^ 2 = 16.81 – 0.81 = 16.

AH = 4 dm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (5.1 + 6.9) * 4/2 = 24 dm2.

Answer: The area of the trapezoid is 24 dm2.

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