Construct the following quadrilaterals.

(i) Quadrilateral LIFT

LI = 4 cm

IF = 3 cm

TL = 2.5 cm

LF = 4.5 cm

IT = 4 cm

Solution:

Construction steps:

Step I: Draw a line segment LI = 4 cm.

Step II: With centre I draw an arc of radius 3 cm.

Step III: With centre L draw another arc of radius 4.5 cm to meet the former arc at F.

Step IV: Join LF and IF.

Step V: Draw an arc with centre L and radius 2.5 cm.

Step VI: Draw another arc with centre I and radius 4 cm to meet the previous arc at T.

Step VII: Join LT and IT.

Hence, LIFT is the required quadrilateral.

(ii) Quadrilateral GOLD

OL = 7.5 cm

GL = 6 cm

GD = 6 cm

LD = 5 cm

OD = 10 cm

Solution:

Constructions steps:

Step I: Draw a line segment OL = 7.5 cm

Step II: With centre O draw an arc of radius 10 cm.

Step III: Draw another arc with centre L and radius 5 cm to meet the previous arc at D.

Step IV: Join OD and LD.

Step V: With centre L draw an arc at D with equal radii of 6 cm to meet each other at G.

Step VI: Join LG and DG.

Hence, GOLD is the required quadrilateral.

(iii) Rhombus BEND

BN = 5.6 cm

DE = 6.5 cm

Solution:

Constructions steps:

(We know that the diagonals of a rhombus bisect each other at the right angle)

Step I: Draw a line segment BN = 5.6 cm.

Step II: At O draw the right bisector of BN.

Step III: Draw two arcs with centre O and radius 12 × DE, i.e., 12 × 6.5 = 3.25 cm to meet the right bisector at D and E.

Step IV: Join BE, EN, ND and BD.

Hence, BEND is the required rhombus.