The bases of the trapezoid are 18 and 10, one of the sides is 4√3, and the angle between
| March 30, 2021 | education
The bases of the trapezoid are 18 and 10, one of the sides is 4√3, and the angle between it and one of the bases is 120 degrees. Find the area of the trapezoid.
From the top of an obtuse angle of 120, draw the height to the base of AD.
In the formed right-angled triangle, the angle НСD = 120 – 90 = 30, then
CosНСD = CH / CD.
Cos30 = CH / 4 * √3.
√3 / 2 = CH / 4 * √3.
CH = 4 * √3 * √3 / 2 = 6 cm.
Determine the area of the trapezoid.
S = (AD + BC) * HC / 2 = (18 + 10) * 6/2 = 84 cm2.
Answer: The area of the trapezoid is 84 cm2.
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