We know that, all sides of a rhombus are equal and the diagonals of a rhombus are perpendicular bisectors of one another. So, to construct a rhombus whose diagonals are 4 cm and 6 cm use the following steps.

1.Draw the diagonal say AC = 4 cm

2.Taking A and C as centres and radius more than ½ AC draw arcs on both sides of the line segment AC to intersect each other.

3.Cut both arcs intersect each other at P and Q, then join PQ.

4.Let PQ intersect AC at the point O. Thus, PQ is perpendicular bisector of AC.

5.Cut off 3 cm lengths from OP and OQ, then we get points B and D.

6.Now, join AB, BC, CD, and DA .

Thus, ABCD is the required rhombus.