1.The square READ with RE = 5.1 cm.

Solution:

Constructions steps:

Step I: Draw a line segment RE = 5.1 cm.

Step II: At E draw an angle of 90° and cut EA = 5.1 cm.

Step III: Draw two arcs from A and R with radius 5.1 cm to cut each other at D.

Step IV: Now, Join RD and AD.

Hence, READ is the required square.

2.A rhombus whose diagonals are 5.2 cm and 6.4 cm long.

Solution:

Constructions steps:

Step I: Draw a line segment AC = 6.4 cm.

Step II: At E draw the right bisector of AC.

Step III: Draw two arcs with centre E and radius = 2.6 cm (we consider 5.2 as diameter) to cut the previous diagonal at B and D.

Step IV: Join AD, AB, BC and DC.

Hence, ABCD is the required rhombus.

3.A rectangle with adjacent sides of lengths 5 cm and 4 cm.

Solution:

Constructions steps:

 Let us we consider two adjacent sides of a rectangle PQRS be PQ = 5 cm and QR = 4 cm.

Now,

Step I: Draw a line segment PQ = 5 cm.

Step II: At Q draw an angle of 90° and cut QR = 4 cm.

Step III: With centre R draw an arc of radius 5 cm.

Step IV: Draw another arc with centre P and radius 4 cm to meet the previous arc at S.

Step V: Join RS and PS.

Hence, PQRS is the required rectangle.

4.A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

Solution:

Construction steps:

Step I: Draw a line segment OK = 5.5 cm.

Step II: Let us draw an angle of 60^o at K and cut KA = 4.2 cm.

Step III: Draw an arc with centre A and radius of 5.5 cm.

Step IV: Draw another arc with centre O and radius 4.2 cm to cut the previous arc at Y.

Step V: Join AY and OY.

Hence, OKAY is the required parallelogram.

The angle at K can be of measure other than 60°. So, it is not a unique parallelogram.