The bases of the trapezoid are 9 and 24, one of the sides is √3 and the angle between them is 120.
| July 10, 2021 | education
The bases of the trapezoid are 9 and 24, one of the sides is √3 and the angle between them is 120. Find the area of the trapezoid.
Let’s build the height BH of the trapezoid ABCD.
Triangle ABH is rectangular, since BH is height, angle ABH = (ABC – 90) = 30.
In a right-angled triangle ABH, leg AH lies opposite angle 30, then AH = AB / 2 = √3 / 2 cm.
By the Pythagorean theorem, we determine the length of the leg BH. BH ^ 2 = AB ^ 2 – AH ^ 2 = 3 – 3/4 = 9/4.
BH = 3/2 = 1.5 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * ВН / 2 = (9 + 24) * 1.5 / 2 = 24.75 cm2.
Answer: The area of the trapezoid is 24.75 cm2.
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