The smaller base of the rectangular trapezoid ABCD is 4 cm, the smaller lateral

The smaller base of the rectangular trapezoid ABCD is 4 cm, the smaller lateral side is 3√3, and the angle D at the base is 60 °. find the area of this trapezoid.

Let’s build the height of the CH trapezoid of the ABСD.

Since the trapezoid is rectangular, and CH is its height, then the quadrilateral ABCH is a rectangle, then CH = AB = 3 * √3 cm, AH = BC = 4 cm.

In a right-angled triangle CDH, tg60 = CH / DH.

DН = СН / tg60 = 3 * √3 / √3 = 3 cm.

Then AD = AH + DH = 4 + 3 = 7 cm.

Determine the area of the trapezoid.

Savsd = (BC + AD) * CH / 2 = (4 + 7) * 3 * √3 / 2 = 33 * √3 / 2 = 16.5 * √3 cm2.

Answer: The area of the trapezoid is 16.5 * √3 cm2.