jmc

Drop perpendiculars from the endpoints of the shorter base of the trapezoid to the other base. This divides the trapezoid into a rectangle and two congruent right triangles. Each of the right triangles has hypotenuse 13 units long and side length $(17-7)/2=5$ units long. Therefore, the height of the trapezoid is $\sqrt{13^2-5^2}=12$ units. The area of the $12\times 7$ rectangle is 84 square units, and the collective area of the two triangles is $2\cdot \frac{1}{2}\cdot 5\cdot 12=60$ square units. The area of the trapezoid is $84+60=\boxed{144}$ square units.