In a rectangular trapezoid, the smaller base is 6, and the smaller side is 2√3. find the area of the trapezoid

In a rectangular trapezoid, the smaller base is 6, and the smaller side is 2√3. find the area of the trapezoid if one of the corners is 120 degrees.

1. Let’s denote the vertices of the trapezoid by the symbols A, B, C, D. AB = 2√3 cm. BC = 6 cm. Angle C = 120 °.

2. Calculate the value of the angle D.

Angle D = 360 ° – 120 ° – 90 ° – 90 ° = 60 °.

3. Draw the perpendicular СН from the vertex С.

4. In the resulting rectangle CH = AB = 2√3 cm. BC = AH = 6 cm.

5. DH / CH = tangent 60 ° = √3. DН / 2√3 = √3. DН = 2√3 x 2 = 2 cm.

6. AD = DH + AH = 6 + 2 = 8 cm.

7. Area of the trapezoid = (BC + AD) / 2 x CH = (6 + 8) x 2√3 = 14 √3 cm ^ 2.

Answer: the area of the trapezoid ABCD is 14 √3 cm ^ 2.