# In a rectangular trapezoid, the smaller base is 3 cm, the larger side

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

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

In a right-angled triangle СDН, we define the values of acute angles. Angle DСН = ВСD – ВСН = 150 – 90 = 60. Angle СDН = (180 – 90 – 60) = 30. The leg СН lies opposite angle 30, then СН = СD / 2 – 4/2 = cm.

DН = СD * Cos30 = 4 * √3 / 2 = 2 * √3 cm.

Quadrangle ABCH is a rectangle, then AH = BC = 3 cm.

AD = AH + DH = 3 + 2 * √3.

Determine the area of the trapezoid.

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

Answer: The area of the trapezoid is 6 + 2 * √3 cm2.

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