NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

 

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 above-mentioned 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.

Go to the respective exercise on clicking the link below

Exercise 5.1

Exercise 5.2

Exercise 5.3

Exercise 5.4

Exercise 5.5

Exercise 5.6

Exercise 5.7

Exercise 5.8

Exercise 5.9

 

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?

Answer:

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?

Answer:

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.

Q4 If A,B,C are three points on a line such that AB = 5 cm, BC = 3 cm and AC = 8 cm, which one of them lies between the other two?

Answer:

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 .

  

Answer:

AD = 4 - 1 = 3

DG = 7 - 4 = 3

Therefore AD = DG

Therefore D is the midpoint of AG.

Q6 If B is the midpoint of AC and C is the midpoint of BD, where A,B,C,D lie on a straight line, say why AB = CD?

Answer:

To Prove:AB=CD

B is the mid point of AC

\therefore \ AB=BC            (i)

C is the mid point of BD

\therefore \ BC=CD            (ii)

From (i) and (ii) we can conclude AB=CD

Hence proved.

Q7 Draw five triangles and measure their sides. Check in each case, if the sum of the lengths of any two sides is always less than the third side.

Answer:

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.

NCERT solutions for Topic: Angles

Q1 What is the angle name for half a revolution?

Answer:

Half a revolution = 180^{\circ}

The angle name for half a revolution is "Straight Angle".

Q2 What is the angle name for one-fourth revolution?

Answer:

One-fourth revolution = 90^{\circ}

The angle name for one-fourth revolution is "Right Angle"

Q3 Draw five other situations of one-fourth, half and three-fourth revolution on a clock.

Answer:

(a) One fourth revolution: From 3\ to\ 6

(b) Half revolution: From 5\ to\ 11

(c) Three fourth revolution: From 9\ to\ 6

(d) Three fourth revolution: From 12\ to\ 9

(e) Half fourth revolution: From 8\ to\ 2

 

NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Exercise: 5.2

Q1 What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes 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

Answer:

(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  \frac{1}{2}   of a revolution, clockwise?

(b) starts at 2 and makes  \frac{1}{2}   of a revolution, clockwise?

(c) starts at 5 and makes  \frac{1}{4}  of a revolution, clockwise?

(d) starts at 5 and makes  \frac{3}{4}   of a revolution, clockwise?

 

Answer:

(a) The hand of a clock will stop at 6 after starting at 12 and making \frac{1}{2}   of a revolution, clockwise.

(b) The hand of a clock will stop at 8 after starting at 2 and making \frac{1}{2}   of a revolution, clockwise.

(c) The hand of a clock will stop at 8 after starting at 5 and making \frac{1}{4}   of a revolution, clockwise.

(d) The hand of a clock will stop at 2 after starting at 5 and making \frac{3}{4}   of a revolution, clockwise. 

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?

Answer:

(a) If we are standing facing east and turn clockwise to face north we have turned through \frac{3}{4}th of a revolution.

(b)  If we are standing facing south and turn clockwise to face east we have turned through \frac{3}{4}th  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

Answer:

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.

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?

Answer:

(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.

NCERT solutions for Topic: Angles

Q1 The hour hand of a clock moves from 12 to 5. Is the revolution of the hour hand more than 1 right angle?

            

Answer:

Yes, the revolution of the hour hand is more than 1 right angle.

For each hour, angle made = \frac{360^{\circ}}{12} = 30^{\circ}

Therefore, when the hour hand moves from 12 to 5, the angle made = 30^{\circ}\times 5= 150^{\circ}

 

Q2 What does the angle made by the hour hand of the clock look like when it moves from 5 to 7. Is the angle moved more than 1 right angle?

            

Answer:

No, the angle is not more than than 1 right angle. 

For each hour, angle made = \frac{360^{\circ}}{12} = 30^{\circ}

Therefore, when the hour hand moves from 5 to 7, the angle made = 30^{\circ}\times 2= 60^{\circ}

 

NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Exercise: 5.3

Q1 Match the following :

(i) Straight angle

(a) Less than one-fourth of a revolution

(ii) Right angle 

(b) More than half a revolution

(iii) Acute angle

(c) Half of a revolution

(iv) Obtuse angle

(d) One-fourth of a revolution

(v) Reflex angle

(e) Between  \frac{1}{4}  and  \frac{1}{2}  of a revolution

 

(f) One complete revolution

Answer:

(i) Straight angle 

(c) Half of a revolution

(ii) Right angle     

(d) One-fourth of a revolution

(iii) Acute angle

(a) Less than one-fourth of a revolution

(iv) Obtuse angle 

  (e) Between  \frac{1}{4}  and  \frac{1}{2}  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 :

            

Answer:

(a) Acute.

(b) Obtuse.

(c) Right.

(d) Reflex.

(e) Straight.

(f) Acute, acute.

 

NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Exercise: 5.4

Q1 What is the measure of (i) a right angle? (ii) a straight angle?

Answer:

(i) 90o

(ii) 180o

Q4 Measure the angles given below using the Protractor and write down the measure.

        Measure the angles given below using the Protractor and write down the measure

 

Answer:

(a) 45o

(b) 125o

(c) 90o

(d) 60o, 90o and 125o

Q5 Which angle has a large measure? First, estimate and then measure.

Measure of Angle A =                                                                                  

Measure of Angle B =                                                                                  

Answer:

Measure of Angle A = 40o

Measure of Angle B = 60o

Q6 From these two angles which has larger measure? Estimate and then confirm by measuring them.

                  

Answer:

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 _____.

(d) When the sum of the measures of two angles is that of a right angle, then each one of them is ______.

(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 _______.

Answer:

(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.

Q8 Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).

             

Answer:

(a) Measure of the given along = 40o 

(b) Measure of the given along = 130o 

(c) Measure of the given along = 65o 

(d) Measure of the given along = 135o 

Q9 Find the angle measure between the hands of the clock in each figure :

             

Answer:

The angle measure between the hands of the clock in each figure is

(a) 90o

(b) 30o

(c) 180o

Q11 Measure and classify each angle :

              

                    

ANGLE

MEASURE

TYPE

\angle AOB

 

 

\angle AOC

 

 

\angle BOC

 

 

\angle DOC

 

 

\angle DOA

 

 

\angle DOB

 

 

 

Answer:

ANGLE

MEASURE

TYPE

\angle AOB

40o

Acute Angle

\angle AOC

125o

Obtuse Angle

\angle BOC

85o

Acute Angle

\angle DOC

95o

Obtuse Angle

\angle DOA

1400

Obtuse Angle

\angle DOB

1800

Straight Angle

 

 

NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Exercise: 5.5

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’.

(d) The letter V.

Answer:

 (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.

Q3 There are two set-squares in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?

Answer:

The angles of the two set squares are

(i) 90o, 60o and 30o

(ii) 90o, 45o, and 45o

Yes they have the common angle measure 90o

Q4 Study the diagram. The line l is perpendicular to line m

(a) Is CE = EG?

(b) Does PE bisect CG?

(c) Identify any two line segments for which PE is the perpendicular bisector.

(d) Are these true?

                    (i) AC > FG

                    (ii) CD = GH

                    (iii) BC < EH.

                

Answer:

(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.

NCERT solutions for Topic: Classification of Triangles

Q1 Try to draw rough sketches of

            (a) a scalene acute angled triangle.

            (b) an obtuse angled isosceles triangle.

Answer:

(a) a scalene acute angled triangle. : 

Scalene : All side of different length

Acute angled : All angles less than 90^{\circ}

 

(b) an obtuse angled isosceles triangle

Isosceles traingle: Only two sides are of equal length

Obtuse angled : At least one angle greater than 90^{\circ}

 

 

NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Exercise: 5.6

Q1 Name the types of following triangles :

(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.

(b) \Delta ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.

(c) \Delta PQR such that PQ = QR = PR = 5 cm.

(d) \Delta DEF with m\angle D=90^{\circ}

(e) \Delta XYZ with m\angle Y=90^{\circ} and XY = YZ.

(f) \Delta LMN with m\angle L=30^{\circ}, m\angle M=70^{\circ} and m\angle N=80^{\circ}

Answer:

(a) Scalene Triangle.

(b) Scalene Triangle.

(c) Equilateral Triangle.

(d) Right-angled Triangle.

(e) Right-angled isosceles Triangle.

(f) Acute angled Triangle.

Q2 Match the following :         

Measure of triangles

Types of triangle

(i) 3 sides of equal length

(a) Scalene

(ii) 2 sides of equal length

(b) Isosceles right-angled 

(iii) All sides of different length

(c) Obtuse angled

(iv) 3 acute angles

(d) Right-angled 

(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

Answer:

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

 

Q3 Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation)

            

Answer:

(a)(i) Acute angled triangle.

    (ii) Isosceles triangle.

(b)(i) Right-angled triangle.

    (ii) Scalane triangle.

(c)(i) Obtuse angled triangle.

    (ii) Isosceles triangle.

(d)(i) Right-angled triangle.

    (ii) Isosceles triangle.

(e)(i) Acute angled triangle.

    (ii) Equilateral triangle.

(f)(i) Obtuse angled triangle.

   (ii) Scalene triangle.

Q2 Using four unequal sticks, as you did in the above activity, see if you can form a quadrilateral such that

             (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

Answer:

(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

Q2 (a) Give reasons for the following: A square can be thought of as a special rectangle.

Answer:

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. 

Answer:

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.

Answer:

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. 

Answer:

Squares, rectangles, parallelograms are all quadrilaterals as they all have four sides.

Q2 (e) Give reasons for the following: Square is also a parallelogram.

Answer:

 Square is also a parallelogram as its opposite sides are parallel.

Q3 A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?

Answer:

Square is the only quadrilateral with sides equal in length and angles equal in measure, therefore, a square is the regular quadrilateral.

NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Exercise: 5.8

Q1 Examine whether the following are polygons. If anyone among them is not, say why?

             

Answer:

(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.

Q2 Name each polygon.

Make two more examples of each of these.

Answer:

(a) Quadrilateral

(b) Triangle

(c) Pentagon

(d) Octagon

 

Q3 Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of triangle you have drawn.

Answer:

We have drawn the regular Hexagon ABCDEF and by joining the vertices B, D and F we have formed the Equilateral Triangle BDF.

Q4 Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.

Answer:

We have made the regular octagon ABCDEFGH and by joining vertices H, C, D and G we have formed the rectangle HCDG

Q5 A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.

Answer:

We have drawn the pentagon ABCDE and by joining its vertices he has drawn the diagonals AC, CE, EB, BD and DA.

NCERT solutions of class 6 maths chapter 5 Understanding Elementary Shapes Topic: Three Dimensional Shapes

 

Q2 A cube is a cuboid whose edges are all of equal length.

           It has ______ faces.

          Each face has ______ edges.

          Each face has ______ vertices.

         

Answer:

 It has \underline{6} faces.        (Three pairs of parallel square faces)  

Each face has \underline{4} edges.         

Each face has \underline{4} vertices

Q3 A triangular pyramid has a triangle as its base. It is also known as a tetrahedron.

              Faces : _______

             Edges : _______

             Corners : _______

             

Answer:

The number of

Faces = 4          (All triangular faces)

Edges = 6             

Corners = 4

 

Q4 A square pyramid has a square as its base.

         Faces : _______

         Edges : _______

         Corners : _______

         

Answer:

In a square pyramid, the number of

Faces = 5          (Four triangular faces and one square face)

Edges = 8          (Four edges of the square base and other four joining at the top)   

Corners = 5

 

Q5 A triangular prism looks like the shape of a Kaleidoscope. It has triangles as its bases.

         Faces : _______

         Edges : _______

        Corners : _______

        

Answer:

Faces =  5 (Two triangular faces and three square faces)

Edges = 9    

Corners = 6

 

NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Exercise: 5.9

Q1 Match the following :

            (a) Cone                                                          (i)     

             (b) Sphere                                                      (ii)            

             (c) Cylinder                                                     (iii)            

             (d) Cuboid                                                       (iv)             

             (e) Pyramid                                                      (v)            

 

Answer:

(a) Cone                                                  (ii)          

(b) Sphere                                               (iv)         

(c) Cylinder                                              (v)     

  (d) Cuboid                                             (iii)      

 (e) Pyramid                                            (i)       

 

Q2 What shape is (a) Your instrument box? (b) A brick? (c) A matchbox? (d) A road-roller? (e) A sweet laddu?

Answer:

the shape of the following things are

(a) Your instrument box- Cuboid

(b) A brick- Cuboid

(c) A matchbox-Cuboid

(d) A road-roller- Cylinder

(e) A sweet laddu-Sphere

 

NCERT solutions for class 6 mathematics chapter-wise

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

CBSE NCERT solutions for class 6 maths chapter 6 Integers

Chapter - 7

NCERT solutions for class 6 maths chapter 7 Fractions

Chapter - 8

Solutions of NCERT for class 6 maths chapter 8 Decimals

Chapter - 9

CBSE NCERT solutions for class 6 maths chapter 9 Data Handling

Chapter -10

NCERT solutions for class 6 maths chapter 10 Mensuration

Chapter -11

Solutions of NCERT for class 6 maths chapter 11 Algebra

Chapter -12

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

Chapter -13

NCERT solutions for class 6 maths chapter 13 Symmetry

Chapter -14

Solutions of NCERT for class 6 maths chapter 14 Practical Geometry

NCERT solutions for class 6 subject wise

NCERT Solutions for class 6 maths

Solutions of NCERT for class 6 science

How to use NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes?

  • You must have covered the previous chapter Basic Geometrical Ideas.
  • Read the conceptual text given in the NCERT textbook.
  • Learn the application of all these concepts in the problems.
  • When you are done with all the above three points, you can practice it.
  • While practicing you can utilize solutions of NCERT for class 6 maths chapter 5 Understanding Elementary Shapes.

Keep learning and working hard!

 

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