In an isosceles trapezoid less than the base is 4 cm, the side is 6 cm and one angle is 150 degrees

In an isosceles trapezoid less than the base is 4 cm, the side is 6 cm and one angle is 150 degrees, find the area of the trapezoid.

1. Draw the height to get the triangle formed by the height and side.
2. Since the trapezium is isosceles, the larger base is equal to the sum of the smaller base and two legs of the triangle.
3. Since one angle is 150 °, the other is 30 °;
4. According to the property of the leg, which lies opposite the angle of 30 °, height = 6/2 = 3 (cm);
5. By the Pythagorean theorem, we find the leg:
√ (32 + 62) = 3√3 (cm);
6. Base:
2 * 3√3 + 4 = 8 + 6√3 (cm);
7. Area:
(8 + 6√3 + 4) / 2 * 3 = 12 + 9√3 (cm²);
Answer: 12 + 9√3 cm².