Question

Construct a quadrliateral ABCD; if:

(i) AB = 4.3 cm, BC = 5.4, CD = 5 cm, DA = 4.8 cm and ∠ ABC = 75∘.

(ii) AB = 6 cm, CD = 4.5 cm, BC = AD = 5 cm and ∠BCD=60∘

(iii) AB = 8 cm, BC = 5.4 cm, AD = 6 cm, ∠A=60∘ and ∠B=75∘.

(iv) AB = 5 cm, BC = 6.5 cm, CD = 4.8 cm, ∠B=75∘ and ∠C=120∘

(v) AB = 6 cm = AC, BC = 4 cm, CD = 5 cm and AD = 4.5 cm.

(vi) AB = AD = 5 cm, BD = 7 cm and BC = DC = 5.5 cm

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Solution

(i) Rough figure is as follow :

Actual figure is constructed as follow :

Steps : 1. Draw AB = 4.3 cm.

2. At B, draw ∠PBA=75∘

3. Cut BC = 5.4 cm.

4. From C & A, draw arcs of radii 5 cm and 4.8 cm respectively which intersect at D.

5. Join AD and DC.

ABCD is the required quadrilateral.

(ii) Rough figure is constructed as follow.

Actual figure is constructed as follow.

Steps : 1. Draw BC = 5 cm.

2. Draw ∠PCB = 60∘ and cut CD = 4.5 cm.

3. From B and D, draw arcs of radii 6 cm and 5 cm respectively which intersect at A.

4. Join AB and AD.

Thus ABCD is the required quadrliateral.

(iii) Rough figure is as follow :-

Actual quadrliateral is constructed with the help of above rough figure.

Steps :

1. Draw AB = 8 cm.

2. At A, draw ∠PAB=60∘ and cut DA = 6 cm.

3. At B, draw ∠QBA=75∘ and cut BC = 5.4 cm.

4. Join DC.

Thus ABCD is the required quadrliateral.

(iv) Rough figure is as shown below.

Actual construction is as follow (using rough fig.)

Steps :

1. Draw BC = 6.5 cm.

2. Draw ∠B=75∘ and cut BA = 5 cm.

3. Draw ∠C=120∘ and cut CD = 4.8 cm.

4. Join AD.

Thus ABCD is the required quadrilateral.

(v) Rough figure is as follow :

Actual quadrliateral is constructed as follow with the help of above rough figure.

Steps : 1. Draw AB = 6 cm.

2. From A and B, draw arcs of radii 6 cm and 4 cm which cut at C.

3. From A and C, draw arcs of radii 4.5 cm and 5 cm respectively which intersect at D.

4. Join BC, CD and DA. Thus ABCD is the required quadrilateral.

(vi) Rough figure is as follow :

Actual construction is as follow (using above rough fig.)

Steps : 1. Draw AB = 5 cm.

2. From A & B draw arcs of radii 5 cm and 7 cm which intersect at D.

3. From B & D draw arcs of radii 5.5 cm each which intersect at C.

4. Join AD, BD, DC and BC.

Thus ABCD is the required quadrilateral.

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