2012 AMC 12B Question 20

A trapezoid has side lengths $3,$ $5,$ $7,$ and $11.$ The sum of all the possible areas of the trapezoid can be written in the form of $r_1\sqrt{n_1} + r_2\sqrt{n_2} + r_3,$ where $r_1,$ $r_2,$ and $r_3$ are rational numbers and $n_1$ and $n_2$ are positive integers not divisible by the square of a prime. What is the greatest integer less than or equal to $$
r_1 + r_2 + r_3 + n_1 + n_2?
$$