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Construction of Rectangle

Example 31: Construct a rectangle PQRS in which PQ = 5.4 cm and diagonal PR = 6.3 cm.
Solution: We know that each angle of rectangle = 90° and opposite sides are equal. Using this
property of rectangle, we may proceed with the given steps.

Steps of construction:
Step 1: Draw a line segment PQ = 5.4 cm.

Step 2: At points P and Q, draw ∠QPX = ∠PQY = 90°.
Step 3: Taking P as centre and radius = 6.3 cm, draw an arc
intersecting QY at R. Join RP.
Step 4: Taking P as centre and radius equal to QR, draw an arc
that will intersect PX at S.

Step 5: Join RS.
Thus, PQRS is the required rectangle.
Construction of Square

Example 32: Construct a square ABCD whose side BC = 4.5 cm.

Solution: Steps of construction:
Step 1: Draw a line segment BC = 4.5 cm.

Step 2: At B, construct ∠CBP = 90°.
Step 3: From BP, cut off BA = 4.5 cm.

Step 4: With C as centre and radius = 4.5 cm, draw an arc.
Step 5: With A as centre and radius = 4.5 cm, draw an arc to
meet the previous arc at D.
Step 6: Join AD and CD.

Thus, ABCD is the required square.
Construction of Rhombus

Example 33: Construct a rhombus ABCD, where AC = 7 cm and BD = 8 cm.

Solution: We know that diagonals of a rhombus are perpendicular bisectors of each other. Using
this property of rhombus, we proceed as follows.

Steps of construction:
Step 1: Draw a line segment AC = 7 cm, and then construct PQ, the
perpendicular bisector of AC.
Step 2: Let PQ and AC intersect each other at O.

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Step 3: Take O as centre and radius = ( × 8) cm = 4 cm. Draw two arcs
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on either side of AC which intersect PQ at the points B and D.
Step 4: Join AB, BC, CD and DA.

Thus, ABCD is the required rhombus.

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