# The bases of the trapezoid are 6 and 30, one of the sides is 7√3, and the angle between

August 16, 2021 | education

| **The bases of the trapezoid are 6 and 30, one of the sides is 7√3, and the angle between it and one of the bases is 120 degrees. Find the S trapezoid.**

Let’s draw the height CH of the trapezoid ABCD.

The sum of the angles of the trapezoid at the lateral sides of the trapezoid is 180, then the angle ADC = 180 – 120 = 60.

From the right-angled triangle CHD, we define its leg CH, which is the height of the trapezoid.

CH = CD * Sin60 = 7 * √3 * √3 / 2 = 10.5 cm.

Determine the area of the trapezoid.

S = (AD + BC) * CH / 2 = (30 + 6) * 10.5 / 2 = 189 cm2.

Answer: The area of the trapezoid is 189 cm2.

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