construct a quadrilateral ABCD in which AB =3.4 cm,

Steps of construction:

Step 1: Draw $A B=3.4 \mathrm{~cm} .$

Step 2: With $B$ as the centre and radius equal to $4 \mathrm{~cm}$, draw an arc.

Step 3: With $A$ as the centre and radius equal to $5.7 \mathrm{~cm}$, draw another arc, cutting the previous arc at $D$.

Step 4: Join $B D$ and $A D$.

Step 5: With $A$ as the centre and radius equal to $8 \mathrm{~cm}$, draw an arc.

Step 6: With $D$ as the centre and radius equal to $3 \mathrm{~cm}$, draw another arc, cutting the previous arc at $C$.

Step 7: Join $A C, C D$ and $B C$.

Thus, ABCD is the required quadrilateral.