Theory:

Let's see how to construct a quadrilateral when four sides and diagonal are given.
Example:
Construct a quadrilateral \(ABCD\), where \(AB = 5 \ cm\), \(BC = 6 \ cm\), \(CD = 4 \ cm\), \(AD = 6 \ cm\) and \(BD = 6.5 \ cm\).
 
Rough diagram:
 
Let us first draw the rough quadrilateral, which will help us to draw a fair quadrilateral.
 
Rou_1.png
 
Fair diagram:
 
Step 1: Draw a line segment \(AB = 5 \ cm\).
 
LI_1.png
 
Step 2: Given \(AD = 6 \ cm\) and \(BD = 6.5 \ cm\). Take \(6 \ cm\) as radius and draw an arc from point \(A\). Then, take \(6.5 \ cm\) as another radius and draw an arc from point \(B\), which cuts the previously drawn arc.
 
LI_2.png
 
Step 3: Mark the two arcs meeting point as \(D\), then join \(AD\) and \(BD\).
 
LI_3.png
 
Step 4: Also, given that \(BC = 6 \ cm\) and \(CD = 4 \ cm\). Take \(6 \ cm\) as radius and draw an arc from point \(B\). Then, take \(4 \ cm\) as another radius and draw an arc from \(D), which cuts the previously drawn arc.
 
LI_4.png
 
Step 5: Mark the two arcs meeting point as \(C\), then join \(BC\) and \(CD\). We obtained the required quadrilateral \(ABCD\).
 
LI_5.png