The smaller base of the rectangular trapezoid ABCD is 4 cm, the smaller lateral side is 3√3

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 ABCD.

Since the trapezoid is rectangular, and CH is its height, then the quadrangle ABCN 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 = (ВС + АD) * СН / 2 = (4 + 7) * 3 * √3 / 2 = 33 * √3 / 2 = 16.5 * √3 cm2.

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