The bases of the trapezoid are 4 cm and 12 cm. The lateral rib, equal to 6 cm, forms an angle of 30

The bases of the trapezoid are 4 cm and 12 cm. The lateral rib, equal to 6 cm, forms an angle of 30 percent with a large base. Find the area of the trapezoid.

Let’s find the height of the trapezoid, after which we will find the area of the figure.
We lower the height from the top-end of the smaller base to the larger base.
It forms a right-angled triangle, in which the hypotenuse is the side of the trapezium, the legs are the height of the trapezoid and the difference between the bases of the trapezium, divided by two. From the sine of the angle at the base of the trapezoid:
sin A = h / c;
h = c * sin A = 6 * 1/2 = 3.
Then the area of the trapezoid is:
S = (a + b) * h / 2 = (4 + 12) * 3/2 = 8 * 3 = 24.