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

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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