6 A uniform lamina OABC is in the shape of a trapezium where O is the origin of the coordinate system in which the points \(A , B\) and \(C\) have coordinates \(( 12,0 ) , ( 12 + p , q )\) and \(( 0 , q )\) respectively.
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1. Determine, in terms of \(p\) and \(q\), the coordinates of the centre of mass of OABC . The point D has coordinates \(( 7.6 , q )\). When OABC is suspended from D , the lamina hangs in equilibrium with BC horizontal.
2. Determine the value of \(p\). When OABC is suspended from C, the lamina hangs in equilibrium with BC at an angle of \(35 ^ { \circ }\) to the downward vertical.
3. Determine the value of \(q\), giving your answer correct to \(\mathbf { 3 }\) significant figures.