7. Constructing a trapezium with two sides and two angles

Construct a trapezium \(PQRS\) in which \(\overline{PQ}\) is parallel to \(\overline{RS}\), \(PQ\) \(=\) \(8.5\) \(cm\), \(QR\) \(=\) \(6.5\) \(cm\), \(\angle PQR\) \(=\) \(75^{\circ}\) and \(\angle QPS\) \(=\) \(110^{\circ}\). Also, find its area.

 

Construction:

 

Step 1: Draw a line segment \(PQ\) \(=\) \(8.5\) \(cm\).

 

Step 2: With \(Q\) as centre, mark an angle \(75^{\circ}\) using a protractor and mark it as \(X\). Join \(QX\).

 

Step 3: With \(Q\) as centre, draw an arc of radius \(6.5\) \(cm\) intersecting \(QX\) at \(R\).

 

Step 4: Draw a line \(RY\) parallel to \(PQ\).

 

Step 5: With \(P\) as centre, mark an angle \(110^{\circ}\) using a protractor and mark it as \(Z\). Join \(PZ\) intersecting \(QY\) at \(S\).

 

Step 6: \(PQRS\) is the required trapezium. The measure of \(RA\) gives the height of the trapezium.