Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.

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Solution

Steps of Construction :

(i) Draw a line segment AB = 3.6 cm.

(ii) With centre A and radius 4.6 cm. and with centre B and radius 3.3 cm. draw arcs intersecting each other at C.

(iii) Join AC and BC.

(iv) Again with centre A and radius 2.7 cm. and centre B and radius 4 cm., draw arcs intersecting each other at D.

(v) Join BD, AD and CD.

ABCD is the required quadrilateral.

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A B C D

A B = 4 c m, B C = 5.6 c m, A C = 7.2 c m

A D = 4.5 c m

B D

Construct a parallelogram ABCD, if :

(i) AB = 3.6 cm, BC = 4.5 cm and $∠ ABC = 120^{\circ} .$

(ii) BC = 4.5 cm, CD = 5.2 cm and $∠ ADC = 75^{\circ} .$

(iii) AD = 4 cm, DC = 5 cm and diagonal BD = 7 cm.

(iv) AB = 5.8 cm, AD = 4.6 cm and diagonal AC = 7.5 cm.

(v) diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is $75^{\circ}$ .

(vi) lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is $45^{\circ}$ .

(vii) lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between then is $60^{\circ}$ .

Construct quadrilateral ABCD given BC = 4.5 cm, AD = 5.5 cm, CD = 5 cm, diagonal AC = 5.5 cm and diagonal BD = 7 cm.

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