# Given a trapezoid ABCD; BC = 5cm, AB = 2cm: Angle BCD = 135 degrees. Find the area of this trapezoid.

January 12, 2021 | education

| Let’s build the height of the CH.

The quadrangle ABCH is rectangular, since the angle A = 90, and CH is the height of the trapezoid, then AH = BC = 5 cm, CH = AB = 2 cm.

The СDН triangle is rectangular. Angle НСD = ВСD – ВСD = (135 – 90) = 45.

Then the angle СDН = (90 – 45) = 45, and therefore, the triangle СDН is rectangular and isosceles, DН = CH = 2 cm.

The length of the segment BP = AH + DН = 5 + 2 = 7 cm.

Determine the area of the trapezoid.

Str = (BC + AD) * CH / 2 = (5 + 7) * 2/2 = 12 cm2.

Answer: The area of the trapezoid is 12 cm2.

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