In a rectangular trapezoid ABCD, the lateral side is AB = 10 cm, the larger base AD

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

1. From the top of the trapezoid, draw the height CH to the larger base AD of the trapezoid ABCD.

2. Since the indicated trapezoid is rectangular, AB = CH = 10 cm.

3. We calculate the length of the segment DН through the tangent of the angle СDН:

CH / DH = tangent 45 ° = 1.

DH = CH = 10 cm.

4. Calculate the length of the segment AH:

AH = AD – DH = 18 – 10 = 8 cm.

AH = BC as opposite sides of the rectangle ABCH. BC = 8 cm.

5. The area of the trapezium ABCD = (BC + AD) / 2 x CH = (8 + 18) / 2 x 10 = 130 cm ^ 2.

Answer: the area of the trapezium ABCD is 130 cm ^ 2.