Construction of Quadrilaterals Class-8 ML Aggarwal ICSE Maths Solutions

Construction of Quadrilaterals Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-14. We provide step by step Solutions of Exercise / lesson-14 Construction of Quadrilaterals Class-8th ML Aggarwal ICSE Mathematics.

Our Solutions contain all type Questions with Exe-14.1 , Exe-14.2, Objective Type Questions ( HOTS ) and Check Your Progress to develop skill and confidence. Visit official Website CISCE  for detail information about ICSE Board Class-8 Mathematics.

Construction of Quadrilaterals Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-14.


–: Select Topic :–  

 Exercise 14.1 ,

Exercise-14.2,

HOTS

Check Your Progress


Exe-14.1 Construction of Quadrilaterals Class-8 ML Aggarwal ICSE Mathematics Solutions

Question 1.
Construct a quadrilateral PQRS where PQ = 4.5 cm, QR = 6 cm, RS = 5.5 cm, PS = 5 cm and PR = 6.5 cm.

Answer

Steps of constructions :
(i) Draw a line segment PR = 6.5 cm.
(ii) With centre P and radius 4.5 cm and with centre R
and radius 6 cm draw arcs intersecting each other at Q.
(iii) Join PQ and QR.
(iv) Similarly with centre P and radius 5 cm and with centre R
and radius 5.5 cm, draw arcs intersecting each other at S.
(v) Join PS and SR.
PQRS is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 1

Question 2.
Construct a quadrilateral ABCD in which AB = 3·5 cm, BC = 5 cm, CD = 5·6 cm, DA = 4 cm and BD = 5·4 cm

Answer

Steps of construction :
(i) Draw AB = 3·5 cm.
(ii) With A as centre and radius = 4 cm,
draw an arc with B as centre and radius = 5·4 cm
draw an arc to meet the previous arc at D. Join AD andBD.
(iii) With B as centre and radius = 5 cm,
draw an arc With D as centre and radius = 5·6 cm,
draw an arc to meet the previous arc at C.
(iv) Join BC and CD, then ABCD is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 2

Question 3.
Construct a quadrilateral PQRS in which PQ = 3 cm, QR = 2·5 cm, PS = 3·5 cm, PR = 4 cm and QS = 5 cm.

Answer

Steps of construction :
(i) Draw PQ = 3 cm.
(ii) With P as centre and radius = 4 cm,
draw an arc with Q as centre and radius = 2·5 cm
draw an arc to meet the previous arc at R.
Join PR and QR.
(iii) With P as centre and radius = 3·5 cm,
draw an arc. With Q as centre and radius = 5 cm,
draw an arc to meet the previous arc at S.
(iv) Join PS, QS and SR.
(v) Hence, PQRS is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 3

Question 4.
Construct a quadrilateral ABCD such that BC = 5 cm, AD = 5.5 cm, CD = 4.5 cm, AC = 7 cm, and BC = 5.5 cm.

Answer

Steps of construction :
(i) Draw a line segment CD = 4.5 cm.
(ii) With centre C and radius of 5.5 cm and with centre D
and radius 7 cm draw arcs intersecting each other at B.
(iii) Join BC and BD.
(iv) Similarly with centre C and radius 5.5 cm
and with centre D and radius 5.5 cm,
draw arcs intersecting each other at A.
(v) Join AC and AD.
(vi) Join AB.
ABCD is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 4

Question 5.
Construct a quadrilateral ABCD given that BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°.

Answer

Steps of construction :
(i) Draw BC = 6 cm.
(ii) At B, construct ∠CBP = 45°.
(iii) At C, construct ∠BCQ = 90°
(iv) From CQ, cut off CD = 4 cm.
(v) At D, construct ∠CDR = 120°.
(vi) Let BP and DR meet at A.
Then ABCD is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 5

Question 6.
Construct a quadrilateral PQRS where PQ = 4 cm, QR = 6 cm, ∠P = 60°, ∠Q = 90° and ∠R = 120°.

Answer

Steps of construction :
(i) Draw a line segment QR = 6 cm.
(ii) At Q, draw a ray QX making an angle of 90°
and cut off QP = 4 cm.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 6
(iii) At P, draw a ray making an angle of 60° and at R,
a ray making an angle 120° which meet each other at S.
PQRS is the required quadrilateral.

Question 7.
Construct a quadrilateral ABCD such that AB = 5 cm, BC = 4·2 cm, AD = 3·5 cm, ∠A = 90°, and ∠B = 60°

Answer

Steps of construction :
(i) Draw AB = 5 cm.
(ii) At A, construct angle A = 90°
(iii) At B, construct angle B = 60°
(iv) With B as centre and 4·2 cm as radius, cut off ∠B atC.
(v) With A as centre and 3·5 cm as radius, cut off ∠A at D.
(vi) Join CD. Then ABCD is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 7

Question 8.
Cosntruct a quadrilateral PQRS where PQ = 4 cm, QR = 5 cm, RS = 4.5 cm, ∠Q = 60° and ∠R = 90°.

Answer

Steps of construction :
(i) Draw a line segment QR = 5 cm.
(ii) At Q, draw a ray QX making an angle of 60°
and cut off QP = 4 cm.
(iii) At R, draw a ray RY making an angle of 90°
and cut off RS. = 4.5 cm.
(iv) Join PS.
PQRS is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 8

Question 9.
Construct a quadrilateral BEST where BE = 3.8 cm, ES = 3.4 cm, ST = 4.5 cm, TB = 5 cm and ∠E = 80°.

Answer

Steps of construction :
(i) Draw a line segment BE = 3.8 cm.
(ii) At E, draw a ray EX making an angle of 80°
and cut off ES = 3.4 cm.
(iii) With centre B and radius 5 cm and
with centre S with radius 4.5 cm,
draw arcs intersecting each other at T.
(iv) Join TB and TS.
BEST is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 9

Question 10.

Construct a quadrilateral ABCD where AB = 4·5 cm, BC = 4 cm, CD = 3·9 cm, AD = 3·2 cm and ∠B = 60°.

Answer

Steps of construction :
(i) Draw AB = 4·5 cm.
(ii) At B, construct ∠ABP = 60°.
(iii) From BP, cut of ∠BC = 4 cm.
(iv) With C as centre, and 3·9 cm as radius draw an arc.
(v) With A as centre and 3·2 cm as radius,
draw an arc to meet the previous arc at D.
(vi) Join AD and CD.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1 10


Construction of Quadrilaterals Class-8 ML Aggarwal ICSE Mathematics Solutions Ex 14.2

Question 1.

Construct a parallelogram ABCD such that AB = 5 cm, BC = 3·2 cm and ∠B 120°.

Answer

Steps of construction :
(i) Draw AB = 5 cm
(ii) At B, Construct angle = 120°
(iii) With B as centre and 3·2 cm as radius cut off ∠B at C.
(iv) With C as centre and AB as radius draw an arc.
(v) With A as centre and 3·2 cm as radius
draw an arc which meets the previous arc at D.
(vi) Join AD and CD.
Then ABCD is required parallelogram
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 1

Question 2.
Construct a parallelogram ABCD such that AB = 4·8 cm, BC = 4 cm and diagonal BD = 5·4 cm.

Answer

Steps of construction :
(i) Construct a triangle ABD.
(ii) With B as centre and 4 cm as radius draw an arc.
(iii) With Das centre and 4·8 cm as radius,
draw an arc which meets the previous arc at C.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 2
(iv) Join CD, BC and AC
(v) Then ABCD is the required parallelogram.

Question 3.
Construct a parallelogram ABCD such that BC = 4·5 cm, BD = 4 cm and AC = 5·6 cm.

Answer

Steps of construction :
(i) Construct a ∆ BOC with BC = 4·5 cm,
BO = \frac{1}{2} × 4 = 2 cm
and OC = \frac{1}{2} AC = \frac{1}{2} × 5.6 = 2·8 cm
(∵ Diagonals of ||gm bisect each other)
(ii) Produce OC to A such that OC = OA
(iii) Produce BO to D such that OD = OB.
(iv) Join AD, then ABCD is the required parallelogram.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 3

Question 4.
Construct a parallelogram ABCD such that AC = 6 cm, BD = 4·6 cm and angle between them is 45°.

Answer

Steps of construction :
(i) Draw AO = \frac{1}{2} AC = 3 cm and produce AO to C
such that OC = OA.
(ii) At O, construct ∠COP = 45°.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 4
(iii) From OP, cut OD = \frac{1}{2} BD = \frac{1}{2} × 4·6 cm = 2·3 cm.
(iv) Produce OD to OB such that OB = OD.
(v) Join AB, BC, CD and DA, then
ABCD is the required to parallelogram.

Question 5.

Construct a rectangle whose adjacent sides are 5·6 cm and 4 cm.

Answer

Steps of construction :
(i) Draw AB = 5·6 cm.
(ii) At B, construct ∠ABP = 90°
(iii) From BP, cut off BC = 4 cm.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 5
(iv) With C as centre and radius = 5·6 cm draw an arc.
(v) With A as centre and radius = 4 cm,
draw an arc to meet the previous arc at D
(vi) Join AD and CD. Then ABCD is the required rectangle

Question 6.
Construct a rectangle such that one side is 5 cm and one diagonal is 6·8 cm.

Answer

Steps of construction :
(i) Draw AB = 5 cm.
(ii) At A, construct ∠BAP = 90°.
(iii) With B as centre and radius = 6·8 cm,
draw an arc to meet AP at D.
(iv) With A as centre and radius = 6·8 cm draw an arc.
(v) With D as centre and radius = 5 cm,
draw an arc to meet the previous arc at C.
(vi) Join BC and CD. Then ABCD is the required rectangle.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 6

Question 7.
Construct a rectangle ABCD such that AB = 4 cm and ∠BAC = 60°.

Answer

Steps of construction :
(i) Draw AB = 4 cm.
(ii) At B, draw ∠ABP = 90°
(iii) At A, construct ∠BAQ = 30°. Let AQ meet BPat D
(iv) With D as centre and radius = 4 cm draw an arc.
(v) With A as centre and radius = BD,
draw an arc to meet the previous arc at C.
(vi) Join AC and CD. Then ABCD is the required rectangle.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 7

Question 8.
Construct a rectangle such that one diagonal is 6-6 cm and angle between two diagonals is 120°.

Answer

Steps of construction :
(i) Draw AO = \frac{1}{2} AC = (\frac{1}{2} × 6·6) cm and produce AO to C
such that OC = OA = 3·3 cm
(ii) At O, construct ∠COB = 120°
(iii) From OB, cut off OB = \frac{1}{2} AC = 3·3 cm.
(iv) Produce BO to D such that OB = OD = 3·3 cm.
(v) Join AB, BC, CD and DA.
Then ABCD is the required rectangle.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 8

Question 9.
Construct a rhombus whose one side is 5 cm and one angle is 45°

Answer

Steps of construction :
(i) Draw AB = 5 cm.
(ii) At A, construct ∠BAP = 45°.
(iii) From AP, cut off AD = 5 cm.
(iv) With B as centre and radius = 5 cm, draw an arc.
(v) With D as centre and radius = 5 cm,
draw an arc to meet the previous arc at C.
(vi) Join BC and CD. Then ABCD is the required rhombus.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 9

Question 10.
Construct a rhombus whose one side is 4·5 cm and one diagonal is 5 cm.

Answer

Steps of construction :
(i) Draw AB = 4·5 cm.
(ii) With A as centre and radius = 4·5 cm, draw an arc.
(iii) With B as centre and radius = 5 cm,
draw an arc to meet the previous arc at D.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 10
(iv) With B as centre and radius = 4·5 cm, draw an arc.
(v) With D as centre and radius = 4·5 cm,
draw an arc to meet the previous arc at C.
(vi) Join AD, BC and CD. Then ABCD is the required rhombus.

Question 11.
Construct a rhombus whose diagonals are 6·8 cm and 5·2 cm.

Answer

Steps of construction :
(i) Draw AC = 6·8 cm.
(ii) Draw 1 bisector PQ of AC to meet it at O.
(iii) From POQ, cut off OB and OD such that
OB = OD = \frac{1}{2} BD = \frac{1}{2} (5·2) cm = 2·6 cm.
(iv) Join AB, BC, CD and DA. Then ABCD is the required rhombus.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 11

Question 12.
Construct a square whose one side is 4·3 cm.

Answer

Steps of construction :
(i) Draw BC = 4·3 cm.
(ii) At B, construct ∠CBP = 90°
(iii) From BP, cut off BA = 4·3 cm.
(iv) With C as centre and radius = 4·3 cm, draw an arc.
(v) With A as centre and radius = 4·3 cm,
draw an arc to meet the previous arc at D.
(vi) Join AD and CD. Then ABCD is the required square.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 12

Question 13.
Construct a square whose one diagonal is 6·2 cm.

Answer

Steps of construction :
(i) Draw AC = 6·2 cm.
(ii) Draw ⊥ bisector PQ of AC to meet it at O.
(iii) From POQ, cut off OB = OD = \frac{1}{2} AC = 3·1 cm.
(iv) Join AB, BC, CD and DA.
Then ABCD is the required square.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2 13


Objective Type Questions, Construction of Quadrilaterals Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-14

(HOTS)

Higher Order Thinking Skills 

Question 1.
Construct a trapezium ABCD in which AB = 7 cm, BC = 4 cm, CD = 3 cm, ∠B = 60° and AB || DC.

Answer

Steps of construction :
(i) Draw a line segment AB = 7 cm.
(ii) At B, draw a ray BX making an angle of 60°
and cut off BC = 4 cm.
(iii) At C draw a line CY parallel to AB
making an angle of 120° and cut off CD = 3 cm.
(iv) Join AD.
ABCD is the required trapezium.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Objective Type Questions 1

Question 2.
Construct a parallelogram PQRS in which PQ = 6 cm, ∠Q = 120° and ∠RPQ = 30°.

Answer

Steps of construction :
(i) Draw a line segment PQ = 6 cm.
(ii) At P, draw a ray making an angle of 30° and at Q
a ray making an angle of 120° intersecting each other at R.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Objective Type Questions 2
(iii) With centre P and radius QR and with centre R
and radius equal to PQ, draw arcs intersecting each other at S.
(iv) Join SP and SR.
PQRS is a required parallelogram.

Question 3.
Construct a rectangle ABCD in which diagonal AC = 7 cm and the diagonals BD and AC intersect at O such that ∠BOC = 45°.

Answer

Steps of construction :
(i) Draw AO= \frac{1}{2}AC = (\frac{1}{2} × 7) cm = 3·5 cm and produce AO to C
such that OC = OA = 3·5 cm.
(ii) At O, construct ∠COP = 45°.
(iii) From OP, cut off OD = \frac{1}{2} AC = 3·5 cm.
produce DO to B such that OB = OD = 3·5 cm.
(iv) Join AB, BC, CD, DA. Then ABCD is the required rectangle.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Objective Type Questions 3


Check Your Progress, Construction of Quadrilaterals Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-14

Question 1.

Construct a quadrilateral ABCD such that AB = 4·5 cm, BC = 4 cm, CD = 3·9 cm, AD = 3·2 cm and ∠B = 60°.

Answer

Steps of construction :
(i) Draw AB = 4·5 cm.
(ii) At B, construct ∠ABP = 60°.
(iii) From BP, cut off BC = 4 cm.
(iv) With C as centre, and 3·9 cm as radius draw an arc.
(v) With A as centre and 3·2 cm as radius,
draw an arc to meet the previous arc at D.
(vi) Join AD and CD.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 1

Question 2.
Construct a quadrilateral ABCD such that AB = 5 cm, BC = 4·2 cm, AD = 3·5 cm, ∠A = 90°, ∠B = 60°.

Answer

Steps of construction :
(i) Draw AB = 5 cm.
(ii) At A, construct angle = 90°
(iii) At Ef’ construct angle = 60°
(iv) With B as centre and 4·2 cm as radius,
draw an arc and mark it as C.
(v) With A as centre and 3·5 cm as radius,
drawn an arc and mark it as D.
(vi) Join CD. Then ABCD is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 2

Question 3.
Construct a quadrilateral ABCD in which AB 3·5 cm, BC = 5 cm, CD = 5·6 cm, DA = 4 cm and BD = 5·4 cm

Answer

Steps of construction :
(i) Draw AB = 3·5 cm.
(ii) With A as centre and radius = 4 cm,
draw an arc and with B as centre and radius = 5·4 cm
draw an arc to meet the previous arc at D. Join AD and BD.
(iii) With B as centre and radius = 5 cm, draw an arc.
With D as centre and radius = 5·6 cm,
draw an arc to meet the previous arc at C.
(iv) Join BC and CD, then ABCD is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 3

Question 4.
Construct a quadrilateral PQRS in which PQ = 3 cm, QR = 2·5 cm, PS = 3·5 cm, PR = 4 cm and QS = 5 cm.

Answer

Steps of construction :
(i) Draw a line PQ = 3 cm.
(ii) With P as centre and 3.5 cm as radius,
draw an arc and with Q as centre and 5 cm as radius,
draw an arc to meet the previous arc at S.
(iii) Join PS and QS.
(iv) With Q as centre and radius = 2.5 cm,
draw an arc and with P as centre and radius = 4 cm,
draw an arc to meet the previous arc at R.
(v) Join PR and QR.
(vi) Join RS, then PQRS is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 4

Question 5.
Construct a quadrilateral ABCD given that BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°.

Answer

Steps of construction :
(i) Draw BC = 6 cm.
(ii) At B, construct ∠CBP = 45°.
(iii) At C, construct ∠BCQ = 90°
(iv) From CQ, cut off CD = 4 cm.
(v) At D, construct ∠CDR = 120°.
(vi) Let BP and DR meet at A.
Then ABCD is the required quadrilateral.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 5

Question 6.
Construct a parallelogram ABCD in which AB = 5.2 cm, AC = 6.5 cm and BD = 7.8 cm.

Answer

Steps of construction :
(i) Draw a line segment AB = 5.2 cm.
(ii) With centre A and radius \frac{6.5}{2} cm = 3.25 cm
and with centre B and radius \frac{7.2}{2} =3.6 cm,
draw arcs intersecting each other at O.
(iii) Join AO and BO and produce them such that OC = AO and OD = BO.
(iv) Join DA, DC, CB.
ABCD is the required parallelogram.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 6

Question 7.
Construct a parallelogram ABCD in which diagonal AC = 4 cm, diagonal BD = 6 cm and angle between diagonals is 75°.

Answer

Steps of construction :
(i) Draw AO = \frac{1}{2} AC = \frac{1}{2} (4 cm) = 2 cm and produce AO to C
such that OC = OA.
(ii) At O, construct ∠COP = 75°.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 7
(iii) From OP, cut OD = \frac{1}{2} BD = \frac{1}{2}(6 cm) = 3 cm.
produce OD to B such that OB = OD.
(iv) Join AB, BC, CD and DA, then ABCD is the required parallelogram.

Question 8.
Construct a rectangle PQRS such that PQ = 3·5 cm and ∠RPS = 75°.

Answer

Steps of construction :
(i) Draw PQ = 3·5 cm.
(ii) At Q, draw ∠PQT = 90°.
(iii) At P, draw angle of 15° which meet QT at R.
(iv) With R as centre and PQ as radius draw an arc.
(v) With P as centre and QR as radius cut the previous arc at S.
Join PS and RS. Then PQRS is the required rectangle.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 8

Question 9.
Construct a rectangle whose one diagonal is 6-8 cm and an angle between two diagonals is 105°.

Answer

Steps of construction :
(i) Draw AO = \frac{1}{2} AC = \frac{1}{2} (6.8 cm) = 3·4 cm and produce AO to C
such that OC = OA = 3·4 cm.
(ii) At O, construct ∠COP = 105°.
(iii) From’OP, cut off OD = \frac{1}{2} AC = \frac{1}{2} × 6·8 = 3·4 cm.
[Because both the diagonals of rectangle are equal]
(iv) Produce OD to B such that OB = OD = 3·4 cm.
(v) Join AB, BC, CD and DA. Then ABCD is the required rectangle.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 9

Question 10.
Construct a rhombus BEST such that BE = 4.5 cm, ET = 6 cm.

Answer

Steps of construction :
(i) Draw a line segment BE = 4.5 cm.
(ii) With centre B and radius 4.5 cm
and with centre E and with radius 6 cm
draw arcs intersecting each other at T.
(iii) Join TB and TE.
(iv) Again with centres E and T,
and radius 4.5 cm from both points,
draw arcs intersecting each other at S.
(v) Join ST and SE.
BEST is the required rhombus.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 10

Question 11.
Construct a rhombus whose diagonals are 7 cm and 5·3 cm.

Answer

Steps of construction :
(i) Draw AC = 7 cm.
(ii) Draw ⊥ bisector PQ of AC to meet it at O.
(iii) From POQ, cut off OB and OD such that OB = OD = \frac{1}{2} BD = \frac{5.3}{2} = 2·65 cm
(iv) Join AB, BC, CD and DA. Then ABCD is the required rhombus.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 11

Question 12.
Construct a square whose one diagonal is 5·8 cm.

Answer

Steps of construction :
(i) Draw AC 5·8 cm.
(ii) Draw perpendicular bisector PQ of AC to meet it at O.
(iii) From POQ, cut off OB = OD such that OB = OD = \frac{1}{2}AC = \frac{1}{2} × 5·8 = 2·9 cm.
(iv) Join AB, BC, CD and DA. Then ABCD is the required square.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress 12

 

—: End of  Construction of Quadrilaterals Class-8 ML Aggarwal Solutions :–

 

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