Slope of a Side of a Trapezium

Geometry Level 3

A trapezium with area $$\frac{417}{16}$$ has three of its sides on the $$x$$-axis, the line $$x = 3$$, and the line $$x = 6$$. The fourth side is contained in the line $$y = mx + \frac{5}{2}$$. The value of $$m$$ can be written as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. Find $$a + b$$.

Details and assumptions

A trapezium has a pair of parallel sides.

×