The bases of the trapezoid are 9 and 24 one of the sides is equal to the root of 3 and the angle between them is 120. Find the area of the trapezoid.
Let’s build the height BH of the trapezoid ABCD.
The ABH triangle is rectangular, since BH is the height, the angle ABH = (ABC – 90) = 30.
In a right-angled triangle ABH, the leg AH lies opposite the 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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