Construct the following quadrilaterals.
(i) Quadrilateral ABCD
AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm, AC = 7 cm
Solution:
Constructions steps:
Step I: Draw a line segment AB = 4.5 cm
Step II: With centre B draw an arc of radius 5.5 cm.
Step III: Draw another arc with centre A of radius 7 cm to meet the previous arc at C.
Step IV: With centre C draw arc of radius 4 cm.
Step V: Draw another arc with centre A and radius 6 cm to cut the former arc at D.
Step VI: Now, join BC, AC, CD and AD.
Hence, ABCD is the required quadrilateral.
(ii) Quadrilateral JUMP
JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm
Solution:
Constructions steps:
Step I: Draw a line segment JU = 3.5 cm.
Step II: With centre J draw an arc of radius 4.5 cm.
Step III: Draw another arc with centre U and radius 6.5 cm to meet the previous arc at P.
Step IV: Join JP and UP.
Step V: With centre U draw an arc of radius 4 cm.
Step VI: Draw another arc with centre P and radius 5 cm to meet the previous arc at M.
Step VII: Join UM and PM.
Hence, JUMP is the required quadrilateral.
(iii) Parallelogram MORE
OR = 6 cm, RE = 4.5 cm, EO = 7.5 cm
Solution:
Constructions steps:
(We know that opposite sides of a parallelogram are equal)
Step I: Draw a line segment OR = 6 cm.
Step II: With centre R draw an arc of radius 4.5 cm.
Step III: Draw another arc with centre O and radius 7.5 cm to meet the previous arc at E.
Step IV: Join RE and OE.
Step V: With centre E draw an arc of radius 6 cm.
Step VI: Draw another arc with centre O and radius 4.5 cm to meet the former arc at M.
Step VII: Join EM and OM.
Hence, MORE is the required parallelogram.
(iv) Rhombus BEST
BE = 4.5 cm, ET = 6 cm
Solution:
Constructions steps:
(We know that all sides of a rhombus are equal)
Step I: Draw BE = 4.5 cm
Step II: With centre B draw an arc of radius 4.5 cm.
Step III: Draw another arc with centre E and radius 6 cm to meet the previous arc at T.
Step IV: Join BT and ET.
Step V: Draw two arcs with centres E and T with equal radii 4-5 cm to meet each other at S.
Step VI: Join ES and TS.
Hence, BEST is the required rhombus.
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