5. Constructing a trapezium with three sides and a diagonal

Construct a trapezium \(ABCD\) in which \(\overline{AB}\) is parallel to \(\overline{CD}\), \(AB\) \(=\) \(9\) \(cm\), \(BC\) \(=\) \(8\) \(cm\), \(CD\) \(=\) \(8\) \(cm\) and \(AC\) \(=\) \(13\) \(cm\).

 

Construction:

 

Step 1: Draw a line segment \(AB\) \(=\) \(9\) \(cm\).

 

Step 2: With \(A\) and \(B\) as centres, draw two arcs of radii \(13\) \(cm\) and \(8\) \(cm\) respectively such that they intersect each other at \(C\).

 

Step 3: Join \(AC\) and \(BC\).

 

Step 4: Draw a line \(CX\) parallel to \(AB\).

 

Step 5: With \(C\) as centre, draw an arc of radius \(8\) \(cm\) intersecting \(CX\) at \(D\).

 

Step 6: Join \(AD\). The measure of \(DE\) gives the height of the trapezium \(ABCD\).