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.

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