In a rectangular trapezoid, the smaller base is 3 cm, the large side is 4 cm

In a rectangular trapezoid, the smaller base is 3 cm, the large side is 4 cm, one of the corners of the trapezoid is 150 degrees. Find the area of the trapezoid.

Let’s draw the height of the CH trapezoid and determine the acute angles of the right-angled triangle CDH.

Angle DСН = (ВСD – ВСН) = (150 – 90) = 60.

Then the angle СDН = (90 – 60) = 30.

The CH leg lies opposite an angle of 30, then CH = CD / 2 = 4/2 = 2 cm.

DH ^ 2 = CD ^ 2 – CH ^ 2 = 16 – 4 = 12.

DН = √12 = 2 * √3 cm.

Quadrilateral ABCN is a rectangle, then AH = BC = 3 cm.

AD = AH + DH = 3 + 2 * √3 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (3 + 3 + 2 * √3) * 2/2 = 6 + 2 * √3 = 2 * (3 + √3) cm2.

Answer: The area of the trapezoid is 2 * (3 + √3) cm2.