Explanation:

Constructions :-

SEE the above attachments

1.

Given That,

BC = 4.5 cm

AD = 5.5 cm

CD = 5 cm

AC = 5.5 cm

BD = 6 cm

Steps of Construction:-

→ Draw a line segment BC with 4.5 cm

→ Draw an arc with 6 cm from B and draw another arc with 5 cm from C .

→ Join B and D , C and D

→ Draw an arc with 5.5 cm from B and draw another arc with 5.5 cm from D .

→ Join D and A , C and A.

This is the required ABCD quadrilateral.

2.

Given that

PQ = 6 cm

QR = 5 cm

We know that

In a Parallelogram OPPOSITE sides are equal and parallel and opposite angles are equal.

Steps of Construction:-

→ Draw a line segment QR with 5 cm

→ CONSTRUCT an angle of 75° at Q.

→ Draw an arc with PQ = 6 cm from Q.

→ Name the intersecting point as P.

→ Construct an angle of 105° at R .

→ Draw a line segment PS with 5 cm

→ Join P and S

This is the required PQRS parallelogram.

3.

Given that

PA = 6 cm

LN = 8 cm

Steps of Construction:-

→ Draw a line segment PA = 6 cm .

→ Construct perpendicular bisectors of PA and join the intersecting points and name them as X and Y

→ The Perpendicular bisector cuts the line segment PA at O.

→ Draw an arc from O with 4 cm on X and On Y.

→ Name the points as L and N

→ Join P and N , N and L , A and N , A and L.

This is the PLAN rhombus .

4.

Given that

length = 5 cm

breadth = 4 cm.

Steps of Construction:-

→ Draw a line segment BC = 5 cm

→ Construct 90° at B and C

→ EXTENDING them to X and Y .

→ Draw arcs from B and C with 4 cm

→ Name the intersecting points as A and D.

→ Join A and D .

This is the required rectangle.

Note :-

There are three steps in the construction.

They are :-

• Rough Diagram
• Construction
• Steps of Construction