NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes All the shapes that you see around yourself are formed using lines and curves. You can see edges, planes, corners, closed curves and open curves in our surroundings. You can organize them into line, line segments, angles, circles triangles, and polygons. Solutions of NCERT for class 6 maths chapter 5 Understanding Elementary Shapes are covering problems related to all the abovementioned figures. You know that all these have different measures and sizes. This chapter deals with the development of tools to measure shapes like triangles, polygons, etc and their sizes. It is one of the most important chapters of this class as well as of the geometry part. So, to have a command on the topic, you, must pay attention to this chapter while studying. Important subtopics covered under this chapter are measuring line segments, angles – ‘Acute’, ‘Obtuse’ and ‘Reflex’, angles – ‘Right’ and ‘Straight’, measuring angles, perpendicular lines, classification of triangles. CBSE NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes is covering the solution from each of the subtopics. In this chapter, there are 45 questions in 9 exercises. Solutions to all these 45 problems are covered comprehensively in solutions of NCERT for class 6 maths chapter 5 Understanding Elementary Shapes. Along with all these, if any time, you are in need of NCERT solutions for other classes and subjects then you can get it through the given link.
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NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Exercise: 5.1
Q1 What is the disadvantage in comparing line segments by mere observation?
The disadvantage in comparing line segments by mere observation is that our estimation may be inaccurate and therefore a divider must be used.
Q2 Why is it better to use a divider than a ruler, while measuring the length of a line segment?
While measuring the length of a line segment using error might creep in due to the thickness and translucency of the ruler and because of angular viewing. We can get rid of these errors using a divider.
AB = 5 cm
BC = 3 cm
AC = 8 cm
Therefore AB + BC = AC
Therefore point B lies between points A and C.
Q5 Verify, whether D is the midpoint of AG .
AD = 4  1 = 3
DG = 7  4 = 3
Therefore AD = DG
Therefore D is the midpoint of AG.
To Prove
B is the mid point of AC
C is the mid point of BD
From (i) and (ii) we can conclude
Hence proved.
After measuring their sides we have found that the sum of lengths of any two sides of a triangle is always greater than the third side.
Half a revolution =
The angle name for half a revolution is "Straight Angle".
Onefourth revolution =
The angle name for onefourth revolution is "Right Angle"
Q3 Draw five other situations of onefourth, half and threefourth revolution on a clock.
(a) One fourth revolution: From
(b) Half revolution: From
(c) Three fourth revolution: From
(d) Three fourth revolution: From
(e) Half fourth revolution: From
(a) 3 to 9 (b) 4 to 7 (c) 7 to 10
(d) 12 to 9 (e) 1 to 10 (f) 6 to 3
(a) Half.
(b) One fourth.
(c) One fourth.
(d) Three fourth.
(e) Three fourth.
(f) Three fourth.
Q2 Where will the hand of a clock stop if it
(a) starts at 12 and makes of a revolution, clockwise?
(b) starts at 2 and makes of a revolution, clockwise?
(c) starts at 5 and makes of a revolution, clockwise?
(d) starts at 5 and makes of a revolution, clockwise?
(a) The hand of a clock will stop at 6 after starting at 12 and making of a revolution, clockwise.
(b) The hand of a clock will stop at 8 after starting at 2 and making of a revolution, clockwise.
(c) The hand of a clock will stop at 8 after starting at 5 and making of a revolution, clockwise.
(d) The hand of a clock will stop at 2 after starting at 5 and making of a revolution, clockwise.
Q3 Which direction will you face if you start facing
(a) east and make of a revolution clockwise?
(b) east and make of a revolution clockwise?
(c) west and make of a revolution anticlockwise?
(d) south and make one full revolution?
(Should we specify clockwise or anticlockwise for this last question? Why not?)
(a) West.
(b) West.
(c) North.
(d) South.
No need to specify clockwise or anticlockwise for the last question as after one complete revolution we would be facing in the same direction.
Q4 What part of a revolution have you turned through if you stand facing
(a) east and turn clockwise to face north?
(b) south and turn clockwise to face east?
(c) west and turn clockwise to face east?
(a) If we are standing facing east and turn clockwise to face north we have turned through of a revolution.
(b) If we are standing facing south and turn clockwise to face east we have turned through of a revolution.
(c) If we are standing facing west and turn clockwise to face east we have turned through half of a revolution.
Q5 Find the number of right angles turned through by the hour hand of a clock when it goes from
(a) 3 to 6 (b) 2 to 8 (c) 5 to 11
(d) 10 to 1 (e) 12 to 9 (f) 12 to 6
Number of right angles turned through by the hour hand of a clock when it goes from
(a) 3 to 6, (b) 2 to 8, (c) 5 to 11, (d) 10 to 1, (e) 12 to 9, (f) 12 to 6 are
(a) 1.
(b) 2.
(c) 2.
(d) 1.
(e) 3.
(f) 2.
Q6 How many right angles do you make if you start facing
(a) south and turn clockwise to west?
(b) north and turn anticlockwise to east?
The number of right angles we can make from the given conditions are
(a) 1.
(b) 3.
(c) 4.
(d) 2.
Q7 Where will the hour hand of a clock stop if it starts
(a) from 6 and turns through 1 right angle?
(b) from 8 and turns through 2 right angles?
(c) from 10 and turns through 3 right angles?
(d) from 7 and turns through 2 straight angles?
(a) Starting from 6 and turns through 1 right angle the hour hand stops at 9.
(b) Starting from 8 and turns through 2 right angle sthe hour hand stops at 2.
(c) Starting from 10 and turns through 3 right angle the hour hand stops at 7.
(d) Starting from 7 and turns through 2 straight angle the hour hand stops at 7.
Yes, the revolution of the hour hand is more than 1 right angle.
For each hour, angle made =
Therefore, when the hour hand moves from 12 to 5, the angle made =
No, the angle is not more than than 1 right angle.
For each hour, angle made =
Therefore, when the hour hand moves from 5 to 7, the angle made =
(i) Straight angle 
(a) Less than onefourth of a revolution 
(ii) Right angle 
(b) More than half a revolution 
(iii) Acute angle 
(c) Half of a revolution 
(iv) Obtuse angle 
(d) Onefourth of a revolution 
(v) Reflex angle 
(e) Between and of a revolution 

(f) One complete revolution 
Answer:
(i) Straight angle 
(c) Half of a revolution 
(ii) Right angle 
(d) Onefourth of a revolution 
(iii) Acute angle 
(a) Less than onefourth of a revolution 
(iv) Obtuse angle 
(e) Between and of a revolution 
(v) Reflex angle 
(b) More than half a revolution 
Q2 Classify each one of the following angles as right, straight, acute, obtuse or reflex :
(a) Acute.
(b) Obtuse.
(c) Right.
(d) Reflex.
(e) Straight.
(f) Acute, acute.
Q1 What is the measure of (i) a right angle? (ii) a straight angle?
(i) 90^{o}
(ii) 180^{o}
(a) The measure of an acute angle < 90°.
(b) The measure of an obtuse angle < 90°.
(c) The measure of a reflex angle > 180°.
(d) The measure of one complete revolution = 360°.
(e) If m A∠ = 53° and m B∠ = 35°, then m A∠ > m B.
(a) True.
(b) False.
(c) True.
(d) True.
(e) True.
(give at least two examples of each).
(a) 30^{o}, 45^{o} and 60^{o}
(b) 120^{o}, 135^{o} and 150^{o}
Q4 Measure the angles given below using the Protractor and write down the measure.
(a) 45^{o}
(b) 125^{o}
(c) 90^{o}
(d) 60^{o}, 90^{o} and 125^{o}
Q5 Which angle has a large measure? First, estimate and then measure.
Measure of Angle A =
Measure of Angle B =
Measure of Angle A = 40^{o}
Measure of Angle B = 60^{o}
Q6 From these two angles which has larger measure? Estimate and then confirm by measuring them.
By estimation followed by confirmation by measurement we know that the second angle is greater.
Q7 Fill in the blanks with acute, obtuse, right or straight :
(a) An angle whose measure is less than that of a right angle is______.
(b) An angle whose measure is greater than that of a right angle is ______.
(c) An angle whose measure is the sum of the measures of two right angles is _____.
(a) An angle whose measure is less than that of a right angle is acute.
(b) An angle whose measure is greater than that of a right angle is obtuse.
(c) An angle whose measure is the sum of the measures of two right angles is straight.
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is acute.
(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be obtuse.
(a) Measure of the given along = 40^{o}
(b) Measure of the given along = 130^{o}
(c) Measure of the given along = 65^{o}
(d) Measure of the given along = 135^{o}
Q9 Find the angle measure between the hands of the clock in each figure :
The angle measure between the hands of the clock in each figure is
(a) 90^{o}
(b) 30^{o}
(c) 180^{o}
Q11 Measure and classify each angle :
ANGLE 
MEASURE 
TYPE 


















ANGLE 
MEASURE 
TYPE 

40^{o} 
Acute Angle 

125^{o} 
Obtuse Angle 

85^{o} 
Acute Angle 

95^{o} 
Obtuse Angle 

140^{0} 
Obtuse Angle 

180^{0} 
Straight Angle 
Q1 Which of the following are models for perpendicular lines :
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter ‘L’.
(a) The adjacent edges of a table top are models for perpendicular lines.
(b) The lines of a railway track are not models for perpendicular lines as they are parallel to each other.
(c) The line segments forming the letter ‘L’ are models for perpendicular lines.
(d) The line segments forming the letter ‘V’ are models for perpendicular lines.
PQ and XY intersect at A
Therefore
The angles of the two set squares are
(i) 90^{o}, 60^{o} and 30^{o}
(ii) 90^{o}, 45^{o,} and 45^{o}
Yes they have the common angle measure 90^{o}
Q4 Study the diagram. The line is perpendicular to line
(c) Identify any two line segments for which PE is the perpendicular bisector.
(i) AC > FG
(ii) CD = GH
(iii) BC < EH.
(a) CE = 5  3 = 2 units
EG = 7  5 = 2 units
Therefore CE = EG.
(b) CE = EG therefore PE bisects CG.
(c) PE is the perpendicular bisector for line segments DF and BH
(d) (i) AC = 3  1 = 2 units
FG = 7  6 = 1 unit
Therefore AC > FG
True
(ii) CD = 4  3 = 1 unit
GH = 8  7 = 1 unit
Therefore CD = GH
True
(iii) BC = 3  2 = 1 unit
EH = 8  5 = 3 units
Therefore BC < EH
True.
Q1 Try to draw rough sketches of
(a) a scalene acute angled triangle.
(b) an obtuse angled isosceles triangle.
(a) a scalene acute angled triangle. :
Scalene : All side of different length
Acute angled : All angles less than
(b) an obtuse angled isosceles triangle
Isosceles traingle: Only two sides are of equal length
Obtuse angled : At least one angle greater than
Q1 Name the types of following triangles :
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) such that PQ = QR = PR = 5 cm.
(a) Scalene Triangle.
(b) Scalene Triangle.
(c) Equilateral Triangle.
(d) Rightangled Triangle.
(e) Rightangled isosceles Triangle.
(f) Acute angled Triangle.
Measure of triangles 
Types of triangle 
(i) 3 sides of equal length 
(a) Scalene 
(ii) 2 sides of equal length 
(b) Isosceles rightangled 
(iii) All sides of different length 
(c) Obtuse angled 
(iv) 3 acute angles 
(d) Rightangled 
(v) 1 right angle 
(e) Equilateral 
(vi) 1 obtuse angle 
(f) Acute angled 
(vii) 1 right angle with two sides of equal length 
(g) Isosceles 
Measure of triangles 
Types of triangle 
(i) 3 sides of equal length 
(e)Equilateral 
(ii) 2 sides of equal length 
(g) Isoscles 
(iii) All sides of different length 
(a) Scalene 
(iv) 3 acute angles 
(f) Acute angled 
(v) 1 right angle 
(d)Right angled 
(vi) 1 obtuse angle 
(c) Obtuse angled 
(vii) 1 right angle with two sides of equal length 
(b) Isoscles right angled 
(a)(i) Acute angled triangle.
(ii) Isosceles triangle.
(b)(i) Rightangled triangle.
(ii) Scalane triangle.
(c)(i) Obtuse angled triangle.
(ii) Isosceles triangle.
(d)(i) Rightangled triangle.
(ii) Isosceles triangle.
(e)(i) Acute angled triangle.
(ii) Equilateral triangle.
(f)(i) Obtuse angled triangle.
(ii) Scalene triangle.
The sides of the quadrilateral are AB, BC, CD, DA
The angles are given by
The other diagonal is AD.
(a) all the four angles are acute.
(b) one of the angles is obtuse.
(c) one of the angles is right angled.
(d) two of the angles are obtuse.
(e) two of the angles are right angled.
(f) the diagonals are perpendicular to one another
(a) all the four angles are acute.
(b) one of the angles is obtuse.
(c) one of the angles is right angled.
(d) two of the angles are obtuse.
(e) two of the angles are right angled.
(f) the diagonals are perpendicular to one another
(a) Each angle of a rectangle is a right angle.
(b) The opposite sides of a rectangle are equal in length.
(c) The diagonals of a square are perpendicular to one another.
(d) All the sides of a rhombus are of equal length.
(e) All the sides of a parallelogram are of equal length.
(f) The opposite sides of a trapezium are parallel.
(a) True.
(b) True.
(c) True.
(d) True.
(e) False.
(f) False.
Q2 (a) Give reasons for the following: A square can be thought of as a special rectangle.
A square can be thought of as a special rectangle as it is a rectangle only but with all sides equal.
Q2 (b) Give reasons for the following: A rectangle can be thought of as a special parallelogram.
A rectangle can be thought of as a special parallelogram as it s a parallelogram only but with all angles equal to ninety degrees.
Q2 (c) Give reasons for the following: A square can be thought of as a special rhombus.
A square can be thought of as a special rhombus because like a rhombus it has all sides equal but all its angles are also equal.
Q2 (d) Give reasons for the following: Squares, rectangles, parallelograms are all quadrilaterals.
Squares, rectangles, parallelograms are all quadrilaterals as they all have four sides.
Q2 (e) Give reasons for the following: Square is also a parallelogram.
Square is also a parallelogram as its opposite sides are parallel.
Square is the only quadrilateral with sides equal in length and angles equal in measure, therefore, a square is the regular quadrilateral.
Q1 Examine whether the following are polygons. If anyone among them is not, say why?
(a) The given figure is not a polygon as it is not a closed figure.
(b) The given figure is a polygon.
(c) The given figure is not a polygon as a polygon is enclosed only by line segments.
(d) The given figure is not a polygon as a polygon is enclosed only by line segments.
Make two more examples of each of these.
(a) Quadrilateral
(b) Triangle
(c) Pentagon
(d) Octagon
We have drawn the regular Hexagon ABCDEF and by joining the vertices B, D and F we have formed the Equilateral Triangle BDF.
We have made the regular octagon ABCDEFGH and by joining vertices H, C, D and G we have formed the rectangle HCDG
We have drawn the pentagon ABCDE and by joining its vertices he has drawn the diagonals AC, CE, EB, BD and DA.
Q2 A cube is a cuboid whose edges are all of equal length.
It has ______ faces.
Each face has ______ edges.
Each face has ______ vertices.
It has faces. (Three pairs of parallel square faces)
Each face has edges.
Each face has vertices
Q3 A triangular pyramid has a triangle as its base. It is also known as a tetrahedron.
Faces : _______
Edges : _______
Corners : _______
The number of
Faces = (All triangular faces)
Edges =
Corners =
Q4 A square pyramid has a square as its base.
Faces : _______
Edges : _______
Corners : _______
In a square pyramid, the number of
Faces = (Four triangular faces and one square face)
Edges = (Four edges of the square base and other four joining at the top)
Corners =
Q5 A triangular prism looks like the shape of a Kaleidoscope. It has triangles as its bases.
Faces : _______
Edges : _______
Corners : _______
Faces = (Two triangular faces and three square faces)
Edges = 9
Corners =
(a) Cone (i)
(b) Sphere (ii)
(c) Cylinder (iii)
(d) Cuboid (iv)
(e) Pyramid (v)
(a) Cone (ii)
(b) Sphere (iv)
(c) Cylinder (v)
(d) Cuboid (iii)
(e) Pyramid (i)
the shape of the following things are
(a) Your instrument box Cuboid
(b) A brick Cuboid
(c) A matchboxCuboid
(d) A roadroller Cylinder
(e) A sweet ladduSphere
Chapters No. 
Chapters Name 
Chapter  1 
NCERT solutions for class 6 maths chapter 1 Knowing Our Numbers 
Chapter  2 
Solutions of NCERT for class 6 maths chapter 2 Whole Numbers 
Chapter  3 
CBSE NCERT solutions for class 6 maths chapter 3 Playing with Numbers 
Chapter  4 
NCERT solutions for class 6 maths chapter 4 Basic Geometrical Ideas 
Chapter  5 
Solutions of NCERT for class 6 maths chapter 5 Understanding Elementary Shapes 
Chapter  6 

Chapter  7 

Chapter  8 

Chapter  9 
CBSE NCERT solutions for class 6 maths chapter 9 Data Handling 
Chapter 10 

Chapter 11 

Chapter 12 
CBSE NCERT solutions for class 6 maths chapter 12 Ratio and Proportion 
Chapter 13 

Chapter 14 
Solutions of NCERT for class 6 maths chapter 14 Practical Geometry 
Keep learning and working hard!