In a rectangular trapezoid, the smaller lateral side is equal to the smaller of the bases and is equal to 12 cm.

In a rectangular trapezoid, the smaller lateral side is equal to the smaller of the bases and is equal to 12 cm. The angle at the base is 135 degrees. Find the area of the trapezoid.

1. AB = BC according to the problem statement.

2. We calculate the value of the angle D:

Angle D = 360 ° – 135 ° – 90 ° – 90 ° = 45 °.

3. Draw a perpendicular from the top of C to the base of AD. In the resulting rectangle

CH = AB = 12 cm, BC = AH = 12 cm.

4. Angle DСН = 180 ° – 45 ° – 90 ° = 45 °. The triangle DСН is isosceles, since the angles at

basis are equal. Therefore, CH = DH = 12 cm.

5.AD = AH + 12 = 12 + 12 = 24 cm.

6. Area of the trapezoid = (BC + AD) / 2 x CH = (12 + 24) / 2 x 12 = 216 cm ^ 2.

Answer: the area of the trapezoid is 216 cm ^ 2.