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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