# Find the area of a rectangular trapezoid with bases 2 and 8 and an acute angle of 45 degrees

May 29, 2021 | education

| From the top of the trapezoid, we will construct the height CH.

Since the trapezoid is rectangular, and CH is height, then the quadrangle ABCH is a rectangle, then AH = BC = 2 cm, and DH = AD – AH = 8 – 2 = 6 cm.

The SND triangle is rectangular, in which one of the acute angles is 45, then the CHD triangle is isosceles, CH = DH = 6 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (2 + 8) * 6/2 = 30 cm2.

Answer: The area of the trapezoid is 30 cm2.

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