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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