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RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
EXERCISE 18.4 PAGE NO: 18.10
1. Construct a quadrilateral ABCD in which AB = 6 cm, BC = 4 cm, CD = 4 
cm, ?B = 95° and ?C = 90°.
Solution:
The given details are AB = 6 cm, BC = 4 cm, CD = 4 cm, ?B = 95° and ?C = 90°. 
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 4cm
Step 2- Construct and angle of 95
o
 at B.
Step 3- Cut an arc of radius 6cm with B as the center to mark that point as A.
Step 4- Construct and angle of 90
o
 at C.
Step 5- Cut an arc of radius 4cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
2. Construct a quadrilateral ABCD where AB = 4.2cm, BC = 3.6 cm, CD = 4.8
cm, ?B = 30° and ?C = 150°.
Solution:
The given details are AB = 4.2cm, BC = 3.6 cm, CD = 4.8 cm, ?B = 30° and ?C = 150°.
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 3.6cm
Step 2- Construct and angle of 30
o
 at B.
Step 3- Cut an arc of radius 4.2cm with B as the center to mark that point as A.
Step 4- Construct and angle of 150
o
 at C.
Step 5- Cut an arc of radius 4.8cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
Page 2


RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
EXERCISE 18.4 PAGE NO: 18.10
1. Construct a quadrilateral ABCD in which AB = 6 cm, BC = 4 cm, CD = 4 
cm, ?B = 95° and ?C = 90°.
Solution:
The given details are AB = 6 cm, BC = 4 cm, CD = 4 cm, ?B = 95° and ?C = 90°. 
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 4cm
Step 2- Construct and angle of 95
o
 at B.
Step 3- Cut an arc of radius 6cm with B as the center to mark that point as A.
Step 4- Construct and angle of 90
o
 at C.
Step 5- Cut an arc of radius 4cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
2. Construct a quadrilateral ABCD where AB = 4.2cm, BC = 3.6 cm, CD = 4.8
cm, ?B = 30° and ?C = 150°.
Solution:
The given details are AB = 4.2cm, BC = 3.6 cm, CD = 4.8 cm, ?B = 30° and ?C = 150°.
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 3.6cm
Step 2- Construct and angle of 30
o
 at B.
Step 3- Cut an arc of radius 4.2cm with B as the center to mark that point as A.
Step 4- Construct and angle of 150
o
 at C.
Step 5- Cut an arc of radius 4.8cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
3. Construct a quadrilateral PQRS in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1
cm, ?Q = 75° and ?R = 120°.
Solution:
The given details are PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ?Q = 75° and ?R = 120°.
Steps to construct a quadrilateral:
Step 1- Draw a line QR = 2.5cm
Step 2- Construct and angle of 75
o
 at Q.
Step 3- Cut an arc of radius 3.5cm with Q as the center to mark that point as P.
Step 4- Construct and angle of 120
o
 at R.
Step 5- Cut an arc of radius 4.1cm with R as the center to mark that point as S.
Step 6- Now join QP, RS and PS
Page 3


RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
EXERCISE 18.4 PAGE NO: 18.10
1. Construct a quadrilateral ABCD in which AB = 6 cm, BC = 4 cm, CD = 4 
cm, ?B = 95° and ?C = 90°.
Solution:
The given details are AB = 6 cm, BC = 4 cm, CD = 4 cm, ?B = 95° and ?C = 90°. 
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 4cm
Step 2- Construct and angle of 95
o
 at B.
Step 3- Cut an arc of radius 6cm with B as the center to mark that point as A.
Step 4- Construct and angle of 90
o
 at C.
Step 5- Cut an arc of radius 4cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
2. Construct a quadrilateral ABCD where AB = 4.2cm, BC = 3.6 cm, CD = 4.8
cm, ?B = 30° and ?C = 150°.
Solution:
The given details are AB = 4.2cm, BC = 3.6 cm, CD = 4.8 cm, ?B = 30° and ?C = 150°.
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 3.6cm
Step 2- Construct and angle of 30
o
 at B.
Step 3- Cut an arc of radius 4.2cm with B as the center to mark that point as A.
Step 4- Construct and angle of 150
o
 at C.
Step 5- Cut an arc of radius 4.8cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
3. Construct a quadrilateral PQRS in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1
cm, ?Q = 75° and ?R = 120°.
Solution:
The given details are PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ?Q = 75° and ?R = 120°.
Steps to construct a quadrilateral:
Step 1- Draw a line QR = 2.5cm
Step 2- Construct and angle of 75
o
 at Q.
Step 3- Cut an arc of radius 3.5cm with Q as the center to mark that point as P.
Step 4- Construct and angle of 120
o
 at R.
Step 5- Cut an arc of radius 4.1cm with R as the center to mark that point as S.
Step 6- Now join QP, RS and PS
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
4. Construct a quadrilateral ABCD given BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 
cm ?D = 100° and ?C = 95
Solution:
The given details are BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 cm ?D = 100° and ?C = 95 
Steps to construct a quadrilateral:
Step 1- Draw a line DC = 4.4cm
Step 2- Construct and angle of 100
o
 at D.
Step 3- Cut an arc of radius 5.6cm with D as the center to mark that point as A.
Step 4- Construct and angle of 9 5
o
 at C.
Step 5- Cut an arc of radius 6.6cm with C as the center to mark that point as B.
Step 6- Now join DA, CB and AB
5. Construct a quadrilateral ABCD in which AD = 3.5 cm, AB = 4.4 cm, BC = 4.7
cm, ?A = 125° and ?B = 120°.
Solution:
The given details are AD = 3.5 cm, AB = 4.4 cm, BC = 4.7 cm, ?A = 125° and ?B =
120°.
Steps to construct a quadrilateral:
Step 1- Draw a line AB = 4.4cm
Step 2- Construct and angle of 125
o
 at A.
Step 3- Cut an arc of radius 3.5cm with A as the center to mark that point as D.
Step 4- Construct and angle of 120
o
 at B.
Step 5- Cut an arc of radius 4.7cm with B as the center to mark that point as C.
Step 6- Now join AD, BC and CD
Page 4


RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
EXERCISE 18.4 PAGE NO: 18.10
1. Construct a quadrilateral ABCD in which AB = 6 cm, BC = 4 cm, CD = 4 
cm, ?B = 95° and ?C = 90°.
Solution:
The given details are AB = 6 cm, BC = 4 cm, CD = 4 cm, ?B = 95° and ?C = 90°. 
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 4cm
Step 2- Construct and angle of 95
o
 at B.
Step 3- Cut an arc of radius 6cm with B as the center to mark that point as A.
Step 4- Construct and angle of 90
o
 at C.
Step 5- Cut an arc of radius 4cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
2. Construct a quadrilateral ABCD where AB = 4.2cm, BC = 3.6 cm, CD = 4.8
cm, ?B = 30° and ?C = 150°.
Solution:
The given details are AB = 4.2cm, BC = 3.6 cm, CD = 4.8 cm, ?B = 30° and ?C = 150°.
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 3.6cm
Step 2- Construct and angle of 30
o
 at B.
Step 3- Cut an arc of radius 4.2cm with B as the center to mark that point as A.
Step 4- Construct and angle of 150
o
 at C.
Step 5- Cut an arc of radius 4.8cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
3. Construct a quadrilateral PQRS in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1
cm, ?Q = 75° and ?R = 120°.
Solution:
The given details are PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ?Q = 75° and ?R = 120°.
Steps to construct a quadrilateral:
Step 1- Draw a line QR = 2.5cm
Step 2- Construct and angle of 75
o
 at Q.
Step 3- Cut an arc of radius 3.5cm with Q as the center to mark that point as P.
Step 4- Construct and angle of 120
o
 at R.
Step 5- Cut an arc of radius 4.1cm with R as the center to mark that point as S.
Step 6- Now join QP, RS and PS
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
4. Construct a quadrilateral ABCD given BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 
cm ?D = 100° and ?C = 95
Solution:
The given details are BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 cm ?D = 100° and ?C = 95 
Steps to construct a quadrilateral:
Step 1- Draw a line DC = 4.4cm
Step 2- Construct and angle of 100
o
 at D.
Step 3- Cut an arc of radius 5.6cm with D as the center to mark that point as A.
Step 4- Construct and angle of 9 5
o
 at C.
Step 5- Cut an arc of radius 6.6cm with C as the center to mark that point as B.
Step 6- Now join DA, CB and AB
5. Construct a quadrilateral ABCD in which AD = 3.5 cm, AB = 4.4 cm, BC = 4.7
cm, ?A = 125° and ?B = 120°.
Solution:
The given details are AD = 3.5 cm, AB = 4.4 cm, BC = 4.7 cm, ?A = 125° and ?B =
120°.
Steps to construct a quadrilateral:
Step 1- Draw a line AB = 4.4cm
Step 2- Construct and angle of 125
o
 at A.
Step 3- Cut an arc of radius 3.5cm with A as the center to mark that point as D.
Step 4- Construct and angle of 120
o
 at B.
Step 5- Cut an arc of radius 4.7cm with B as the center to mark that point as C.
Step 6- Now join AD, BC and CD
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
6. Construct a quadrilateral PQRS in which ?Q = 45° and ?R = 90°, QR = 5
cm, PQ = 9 cm and RS = 7 cm.
Solution:
The given details are ?Q = 45° and ?R = 90°, QR = 5 cm, PQ = 9 cm and RS = 7 cm.
Steps to construct a quadrilateral:
Step 1- Draw a line QR = 5cm
Step 2- Construct and angle of 45
o
 at Q.
Step 3- Cut an arc of radius 9cm with Q as the center to mark that point as P.
Step 4- Construct and angle of 90
o
 at R.
Step 5- Cut an arc of radius 7cm with R as the center to mark that point as S.
Step 6- Now join QP, RS
Since the line segment QP and RS are not intersecting at each other, quadrilateral cannot
be formed.
Page 5


RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
EXERCISE 18.4 PAGE NO: 18.10
1. Construct a quadrilateral ABCD in which AB = 6 cm, BC = 4 cm, CD = 4 
cm, ?B = 95° and ?C = 90°.
Solution:
The given details are AB = 6 cm, BC = 4 cm, CD = 4 cm, ?B = 95° and ?C = 90°. 
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 4cm
Step 2- Construct and angle of 95
o
 at B.
Step 3- Cut an arc of radius 6cm with B as the center to mark that point as A.
Step 4- Construct and angle of 90
o
 at C.
Step 5- Cut an arc of radius 4cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
2. Construct a quadrilateral ABCD where AB = 4.2cm, BC = 3.6 cm, CD = 4.8
cm, ?B = 30° and ?C = 150°.
Solution:
The given details are AB = 4.2cm, BC = 3.6 cm, CD = 4.8 cm, ?B = 30° and ?C = 150°.
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 3.6cm
Step 2- Construct and angle of 30
o
 at B.
Step 3- Cut an arc of radius 4.2cm with B as the center to mark that point as A.
Step 4- Construct and angle of 150
o
 at C.
Step 5- Cut an arc of radius 4.8cm with C as the center to mark that point as D.
Step 6- Now join BA, CD and AD
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
3. Construct a quadrilateral PQRS in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1
cm, ?Q = 75° and ?R = 120°.
Solution:
The given details are PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ?Q = 75° and ?R = 120°.
Steps to construct a quadrilateral:
Step 1- Draw a line QR = 2.5cm
Step 2- Construct and angle of 75
o
 at Q.
Step 3- Cut an arc of radius 3.5cm with Q as the center to mark that point as P.
Step 4- Construct and angle of 120
o
 at R.
Step 5- Cut an arc of radius 4.1cm with R as the center to mark that point as S.
Step 6- Now join QP, RS and PS
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
4. Construct a quadrilateral ABCD given BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 
cm ?D = 100° and ?C = 95
Solution:
The given details are BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 cm ?D = 100° and ?C = 95 
Steps to construct a quadrilateral:
Step 1- Draw a line DC = 4.4cm
Step 2- Construct and angle of 100
o
 at D.
Step 3- Cut an arc of radius 5.6cm with D as the center to mark that point as A.
Step 4- Construct and angle of 9 5
o
 at C.
Step 5- Cut an arc of radius 6.6cm with C as the center to mark that point as B.
Step 6- Now join DA, CB and AB
5. Construct a quadrilateral ABCD in which AD = 3.5 cm, AB = 4.4 cm, BC = 4.7
cm, ?A = 125° and ?B = 120°.
Solution:
The given details are AD = 3.5 cm, AB = 4.4 cm, BC = 4.7 cm, ?A = 125° and ?B =
120°.
Steps to construct a quadrilateral:
Step 1- Draw a line AB = 4.4cm
Step 2- Construct and angle of 125
o
 at A.
Step 3- Cut an arc of radius 3.5cm with A as the center to mark that point as D.
Step 4- Construct and angle of 120
o
 at B.
Step 5- Cut an arc of radius 4.7cm with B as the center to mark that point as C.
Step 6- Now join AD, BC and CD
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
6. Construct a quadrilateral PQRS in which ?Q = 45° and ?R = 90°, QR = 5
cm, PQ = 9 cm and RS = 7 cm.
Solution:
The given details are ?Q = 45° and ?R = 90°, QR = 5 cm, PQ = 9 cm and RS = 7 cm.
Steps to construct a quadrilateral:
Step 1- Draw a line QR = 5cm
Step 2- Construct and angle of 45
o
 at Q.
Step 3- Cut an arc of radius 9cm with Q as the center to mark that point as P.
Step 4- Construct and angle of 90
o
 at R.
Step 5- Cut an arc of radius 7cm with R as the center to mark that point as S.
Step 6- Now join QP, RS
Since the line segment QP and RS are not intersecting at each other, quadrilateral cannot
be formed.
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
7. Construct a quadrilateral ABCD in which AB = BC = 3 cm, AD = 5 cm, ?A = 90°
and ?B = 105°.
Solution:
The given details are AB = BC = 3 cm, AD = 5 cm, ?A = 90° and ?B = 105°.
Steps to construct a quadrilateral:
Step 1- Draw a line AB = 3cm
Step 2- Construct and angle of 90
o
 at A.
Step 3- Cut an arc of radius 5cm with A as the center to mark that point as D.
Step 4- Construct and angle of 105
o
 at B.
Step 5- Cut an arc of radius 3cm with B as the center to mark that point as C.
Step 6- Now join AD, BC and CD
8. Construct a quadrilateral BDEF, where DE = 4.5 cm, EF = 3.5 cm, FB = 6.5
cm, ?F = 50° and ?E = 100°.
Solution:
The given details are DE = 4.5 cm, EF = 3.5 cm, FB = 6.5 cm, ?F = 50° and ?E = 100°.
Steps to construct a quadrilateral:
Step 1- Draw a line EF = 3.5cm
Step 2- Construct and angle of 100
o
 at E.
Step 3- Cut an arc of radius 4.5cm with E as the center to mark that point as D.
Step 4- Construct and angle of 50
o
 at F.
Step 5- Cut an arc of radius 6.5cm with F as the center to mark that point as B.
Step 6- Now join DE, FB and DB

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