The lateral side of the trapezoid is 5, and one of the corners adjacent to it is 30 °. Find the area of the trapezoid if its bases are 3 and 9.

The area of the trapezoid is equal to the product of half the sum of the bases in height. We know the reasons, we will find the height of the trapezoid.
Draw the height as shown in the figure. The resulting triangle is rectangular. By definition of the sine, we can write: sin30 ° = h / 5 => h = 5 * sin30 °, sin30 ° = 1/2 (tabular value).
h = 5 * 1/2 = 2.5.
Straps = (3 + 9) / 2 * 2.5 = 15
Answer: the area of the trapezoid is 15

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