# The bases of the trapezoid are 9 and 24 one of the sides is equal to the root of 3

July 28, 2021 | education

| **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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