The bases of the trapezoid are 18 and 12, one of the sides is 6, and the sine of the angle between
| April 11, 2021 | education
The bases of the trapezoid are 18 and 12, one of the sides is 6, and the sine of the angle between it and one of the bases is 1/3. Find the area of the trapezoid.
In trapezoid ABCD of the base AD = 18, BC = 12, lateral side AB = 6; sin A = 1/3, BH – height;
The area of the trapezoid is equal to half the product of the sum of the bases and the height:
S = 1/2 (AD + BC) * BH;
sin A = BH / AB; BH = AB * sin A = 6 * 1/3 = 2;
S = 1/2 (18 + 12) * 2 = 30.
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