6. Constructing a trapezium with three sides and an angle

Construct a trapezium \(FINE\) in which \(\overline{FI}\) is parallel to \(\overline{NE}\), \(FI\) \(=\) \(8.5\) \(cm\), \(IN\) \(=\) \(6.5\) \(cm\), \(FE\) \(=\) \(7.5\) \(cm\) and \(\angle FIN\) \(=\) \(75^{\circ}\) at \(I\).

 

Construction:

 

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

 

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

 

Step 3: With \(I\) as centre, draw an arc of radius \(6.5\) \(cm\) intersecting \(IX\) at \(N\).

 

Step 4: Draw a line \(NY\) parallel to \(FI\).

 

Step 5: With \(F\) as centre, draw an arc of radius \(7.5\) \(cm\) intersecting \(NY\) at \(E\).

 

Step 6: Join \(FE\). The measure of \(NA\) gives the height of the required trapezium \(FINE\).