A rectangular trapezoid has a smaller base 3cm, a larger side 4cm, and one of the corners = 150 degrees. Find the area.

Let’s build the height of the CH trapezoid ABCD. In a right-angled triangle СDН, we determine the value of the angle DСН. The angle DСН = ВСD – ВСН = 150 – 90 = 60, then the angle СDН = 90 – 60 = 30.

The CH leg lies opposite an angle of 30, then CH = CD / 2 = 4/2 = 2 cm.

In a right-angled triangle CDH, according to the Pythagorean theorem, DH ^ 2 = CD ^ 2 – CH ^ 2 = 16 – 4 = 12 cm.

DН = 2 * √3 cm.

AH = BC = 3 cm, since ABCH is a rectangle, then AD = AH + DH = 3 + 2 * √3 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (3 + 3 + 2 * √3) * 2/2 = 6 + 2 * √3 cm2.

Answer: The area of the trapezoid is 6 + 2 * √3 cm2.