# In a rectangular trapezoid ABCD, the lateral side AB = 10cm. Bigger base AD = 18cm, angle D

In a rectangular trapezoid ABCD, the lateral side AB = 10cm. Bigger base AD = 18cm, angle D = 45. Find the area of the trapezoid.

Let us draw the height CH from the top of the obtuse angle C. Since the trapezoid is rectangular, and CH is the height of the trapezoid, the quadrilateral ABCH is a rectangle. Then CH = AB = 10 cm.

Triangle СDH is rectangular, in which the angle DCH = 180 – СHD – СDH = 180 – 90 – 45 = 450.

Then the triangle CDH is rectangular and isosceles, DH = CH = 10 cm.

The length of the segment AH = AD – DH = 18 – 10 = 8 cm, then BC = AH = 8 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (8 + 18) * 10/2 = 130 cm2.

Answer: The area of the trapezoid is 130 cm2.

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