Calculate the area of a trapezoid ABCD with bases AD and BC if AD = 24cm, BC = 16cm

Calculate the area of a trapezoid ABCD with bases AD and BC if AD = 24cm, BC = 16cm, angle A = 45 degrees, angle D = 90 degrees.

1. From the corner B of the trapezoid, we lower the height of the VO, which divided the larger base into two parts, one of which is equal to the smaller base. Let’s define the value of another.
24 – 16 = 8 centimeters.
2. In the formed triangle ABO, the angle O is straight, angle A is 45 °, angle B is 180 – (90 + 45) = 45 °. Equal sides lie opposite equal angles. This means that the height of the trapezoid is 8 centimeters.
3. Find what is the area of the trapezoid.
(24 + 16) / 2 * 8 = 160 cm².
Answer: 160 square centimeters.