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

In a rectangular trapezoid, the smaller base is 6 cm, and the smaller side is 2√3. Find the area of a trapezoid if one of its angles is 120 degrees.

Let’s draw from the top С the height СН. In a right-angled triangle СDН the angle DСН = ВСD – ВСН = 120 – 90 = 30. Then tg30 = DH / СН.

DН = СН * tg30 = 2 * √3 * (1 / √3) = 2 cm.

Since the quadrangle ABCН is a rectangle, then AH = BC = 6 cm, then AD = AH + DDH = 6 + 2 = 8 cm.

Let’s calculate the area of the trapezoid. Savsd = (BC + AD) * AB / 2 = (6 + 8) * 2 * √3 / 2 = 14 * √3 cm2.

Answer: The area of the trapezoid is 14 * √3 cm2.