STEPS:
i) Draw a line segment TE = 8 cm.
ii) Draw the perpendicular bisector XY to TE let it bisect TE at O.
iii) With O as centre, draw arcs of radius 4 cm on either side of O which cut OX at Sand OY at R.
iv) Join TR, RE, ES and ST.
v) REST is the required square
Calculation of area
Area of square REST = a².sq units. 
= 5.7\(\times\)5.7 = 32.49 cm².

STEPS:
(i) Draw a line segment SA = 5.6 cm.
(ii) At S, Construct SX 丄SA.
(iii) With S as centre, draw an arc of radius 4.4 cm and let it cut SX at D.
(iv) With A and D as centres, draw arcs of radii 4.4 cm and 5.6 cm respectively and let them cut at N.
(v) Join DN and AN.
(vi) SAND is the required rectangle
Calculation of area
Area of rectangle HAND = I x b sq units
= 5.6 x 4.4 = 24.64 cm^2..

STEPS:
(i) Draw a line segment AK = 7.5 cm.
(ii) At A, make \(\angle KAX=\angle KAY={ 40 }^{ 0 }\) on either side of AK.
(iii) At K, make \(\angle AKP=\angle AKQ={ 40 }^{ o }\) on either side of AK.
(iv) Let AX and KP cut at M and AY and KQ cut at R.
(v) MARK is the required rhombus
Calculation of area
Area of rhombus MARK = \(\cfrac { 1 }{ 2 } \times { d }_{ 1 }\times { d }_{ 2 }\) sq.units 
 

(i) If DE = 44 then DM = ?
M is the Midpoint of DE 
DM + ME = 44 (DM = ME)
DM + DM = 44
2 DM = 44
DM = 22 
(ii) PD: PN = 2: 1
2 Part = 12

PN = 6
(iii) If DO = 8, then FD = ?
O is the midpoint of DF.
FD = DO + OF
= DO + OD
= 2 OD
= 2 x 8
FD = 16
(iv) If OE = 36 then EP = ?
EP : PO = 2  :1
\(\frac{\mathrm{EP}}{\mathrm{PO}}=\frac{2}{1}\)
EP = 2 PO
EO - OP = 2PO
EO = 3 PO
36 =  3 PO
PO = 12
EP = EO - PO
= 36 - 12
= 24

\(\angle Y=2\times { 30 }^{ 0 }={ 60 }^{ o }\) 
\(\angle Z=2\times { 40 }^{ o }={ 80 }^{ o }\) 
\(\angle X+\angle Y+\angle Z={ 180 }^{ 0 }\) 
\(\angle X+{ 60 }^{ o }+{ 80 }^{ o }={ 180 }^{ o }\) 
\(\angle X+{ 140 }^{ o }={ 180 }^{ o }\) 
\(\angle X={ 180 }^{ o }-{ 140 }^{ o }={ 40 }^{ o }\) 
\(\angle YXZ={ 40 }^{ o }\)