Construct a rhombus with side 6 cm and one diagonal 8 cm.

Steps of construction :

Step 1: Draw $\mathrm{AC}=8 \mathrm{~cm} .$

Step 2: With $\mathrm{A}$ as the centre and radius $=6 \mathrm{~cm}$, draw arcs on both sides.

Step 3: With $\mathrm{C}$ as the centre and radius $=6 \mathrm{~cm}$, draw arcs on both sides, intersecting the previous arcs at points B and D.

Step 4: Join $\mathrm{BD}=8.9 \mathrm{~cm} .$

Thus, $\mathrm{ABCD}$ is the required rhombus.