Given: diagonal = 8 cm


(i) Draw a line segment RM = 8 cm.
(ii) Draw the perpendicular bisector XY to RM. Let it bisect RM at O.
(iii) With O as centre, draw arcs of radius 4 cm on either side of O which cut OX at P and OY at A.
(iv) Join RA, AM, MP and PR.
(v) RAMP is the required square.
Calculation of area:
Area of square RAMP = a² sq.units
= 5.7 x 5.7 = 32.49sq.cm

Given: LI = 6 cm and IE = 7 cm

Steps:
(i) Draw a line segment LI = 6 cm.
(ii) At L, construct LX ⊥LI .
(iii) With I as centre, draw an arc of radius 7 cm and let it cut LX at E.
(iv) With I as centre and LE as radius draw an arc. Also, with E as centre and LI as radius draw an another arc. Let them cut at M.
(v) Join IM and EM.
(vi) LIME is the required rectangle.
Calculation of area:
Area of rectangle LIME = l x b sq.units
= 6 x 3.6 = 21.6 sq.cm

Given: BE = 5 cm and BN = 3 cm

Steps:
(i) Draw a line segment BE = 5 cm.
(ii) At B, construct BX ⊥BE .
(iii) With B as centre, draw an arc of radius 3 cm and let it cut BX at N.
(iv) With E and N as centres, draw arcs of radii 3 cm and 5 cm respectively and let them cut at A.
(v) Join EA and NA.
(vi) BEAN is the required rectangle
Calculation of area:
Area of rectangle BEAN = l × b sq.units
= 5 x 3 = 15sq.cm

Given: NS = 9 cm and ET = 8 cm


Steps
(i) Draw a line segment NS = 9 cm.
(ii) Draw the perpendicular bisector XY to NS. Let it cut NS at O.
(iii) With O as centre, draw arcs of radius 4 cm on either side of
O which cut OX at T and OY at E.
(iv) Join NE, ES, ST and TN.
(v) NEST is the required rhombus
Calculation of area:
Area of rhombus NEST=\(\cfrac { 1 }{ 2 } \times { d }_{ 1 }\times { d }_{ 2 }sq.units\) 
=\(\cfrac { 1 }{ 2 } \times { d }_{ 1 }\times { d }_{ 2 }sq.units\) 
= \(\cfrac { 1 }{ 2 } \times 9\times 8=36sq.cm\)

Given: RO = 5 cm and RS = 8 cm


Steps:
(i) Draw a line segment RO = 5 cm.
(ii) With R and O as centres, draw arcs of radii 8 cm and 5 cm respectively and let them cut at S.
(iii) Join RS and OS.
(iv) With R and S as centres, draw arcs of radius 5 cm each and let them cut at E.
(v) Join RE and SE.
(vi) ROSE is the required rhombus.
Calculation of area:
Area of rhombus ROSE =\(\cfrac { 1 }{ 2 } \times { d }_{ 1 }\times { d }_{ 2 }\) sq.units
= \(\cfrac { 1 }{ 2 } \times 8\times 6=24sq.cm\)