The larger base of a rectangular trapezoid is 4, less than 3. Find the area of the trapezoid if one of the corners is 150 degrees.
From the vertex C of the trapezoid, we will construct the height CH.
Since the trapezoid is rectangular, and CH is the height, then the quadrangle ABCH is a rectangle, and then AH = BC = 3 cm, and the triangle CDH is rectangular.
DН = АD – АН = 4 – 3 = 1 cm.
In a right-angled triangle СDН the angle DСН = ВСD – ВСН = 150 – 90 = 60.
Tg60 = DH / CH.
CH = DH / tg60 = 1 / √3 = √3 / 3 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * СН / 2 = (3 + 4) * (√3 / 3) / 2 = 7 * √3 / 6 cm2.
Answer: The area of the trapezoid is 7 * √3 / 6 cm2.
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