In trapezoid ABCD, angle A = 60 degrees, angle D = 45 degrees, base BC = 5 cm

| January 30, 2021 | education

In trapezoid ABCD, angle A = 60 degrees, angle D = 45 degrees, base BC = 5 cm, BF and CE-trapezoid height, ED = 4 cm. Find the area of the trapezoid.

Since CE and BF are trapezoid heights, the triangles CDE and ABF are rectangular.

In a right-angled triangle СDE, one of the acute angles is 45, then this triangle is isosceles, DE = CE = 4 cm.

Then BF = CE = 4 cm.

In a right-angled triangle ABF, the angle BAF = 60, then tg60 = BF / AF.

AF = BF / tg60 = 4 / √3 = 4 * √3 / 3cm.

Quadrilateral BCEF rectangle, then ЕF = BC = 5 cm.

AD = AF + EF + DE = (4 * √3 / 3) + 5 + 4 = 9 + 4 * √3 / 3) = (27 + 4 * √3) / 3.

Then Savsd = (ВС + AD) * CE / 2 = (5 + (27 + 4 * √3) / 3) * 4/2 = ((15 + 27 + 4 * √3) / 3) * 2 = ( 84 + 8 * √3) / 3 cm2.

Answer: The area of the trapezoid is (84 + 8 * √3) / 3 cm2.



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