In a trapezoid with bases 3 and 9, the side is 3, the angle adjacent to it is 30. you need to find the area of the trapezoid.

Let us draw the height of the ВН from the apex of the obtuse angle B. In the formed right-angled triangle AВН, the angle ВAН = 30 by condition, then the length of the leg of the ВН, lying opposite it, is equal to half of the hypotenuse AB.

ВН = AB / 2 = 3/2 = 1.5 cm.

Determine the area of the trapezium ABCD.

Savsd = (ВС + АD) * ВН / 2 = (3 + 9) * 1.5 / 2 = 18/2 = 9 cm2.

Answer: The area of the trapezoid is 9 cm2.