In trapezoid ABCD, AB is parallel to CD, and AB < CD. The base CD has a length of 8. The legs AD and BC have lengths of 7, and the diagonal BD has a length of 9. Find the area of the trapezoid.

The area of a trapezoid is equal to the average of the lengths of its bases multiplied by its height. In this case, the bases have lengths of 7 and 8, and the height is 7. Therefore, the area of the trapezoid is (7+8)/2⋅7=63.