### 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. Fair diagram:

Step 1: Draw a line segment $$AB = 5 \ cm$$. 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. Step 3: Mark the two arcs meeting point as $$D$$, then join $$AD$$ and $$BD$$. 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. Step 5: Mark the two arcs meeting point as \(C$$, then join $$BC$$ and $$CD$$. We obtained the required quadrilateral $$ABCD$$. 