# 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 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.

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.

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.

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.

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.

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.

(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.

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.

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.

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.

### 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

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.

(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.

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°.

(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.

(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.

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.

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.

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.

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.

(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.

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.

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.

### 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.

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.

(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.

### 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.

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.

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.

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.

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.

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.

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°.

(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.

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.

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.

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.

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.

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

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