# NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

**NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes** - 6th class students can access NCERT Class 6 Maths Solutions Chapter 5 in this article. All the shapes that you see around yourself are formed using lines and curves. Class 6 NCERT maths solutions chapter 5 are covering problems related to line segments, circle and other shapes. NCERT Maths Class 6 chapter 5 solutions are prepared, based on the problems available in NCERT Class 6 syllabus. It is one of the most important chapters of this class as well as of the geometry part. So students should prepare well and refer to NCERT Solutions for Class 6 Maths Chapter 5, in case of any doubt. CBSE NCERT class 6 maths solutions chapter 5 is covering the solution of all the subtopics. In this chapter of NCERT, there are 45 questions in 9 exercises. NCERT Maths Class 6 Chapter 5 Solutions to all these 45 problems are covered and provided below. Check NCERT solutions for other classes and subjects.

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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?

** 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.

** 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.

** Answer: ** To Prove

B is the midpoint of AC

C is the midpoint of BD

From (i) and (ii) we can conclude

Hence proved.

** 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 class 6 maths topic: angles **

** Q1 ** What is the angle name for half a revolution?

** Answer: ** Half a revolution =

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

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

** Answer: ** One-fourth revolution =

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

(b) Half revolution: From

(c) Three fourth revolution: From

(d) Three fourth revolution: From

(e) Half fourth revolution: From

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

(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 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?

** Answer: **

(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 anti-clockwise?

(d) south and make one full revolution?

(Should we specify clockwise or anti-clockwise for this last question? Why not?)

** Answer: **

(a) West.

(b) West.

(c) North.

(d) South.

No need to specify clockwise or anti-clockwise 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?

** Answer: **

(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

** 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.

** Q6 ** How many right angles do you make if you start facing

(a) south and turn clockwise to west?

(b) north and turn anti-clockwise to east?

(c) west and turn to west?

(d) south and turn to north?

** Answer: ** 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?

** 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 angles the hour hand stops at 2.

(c) Starting from 10 and turns through 3 right angles the hour hand stops at 7.

(d) Starting from 7 and turns through 2 straight angles the hour hand stops at 7.

** NCERT solutions for class 6 maths topic: Angles **

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

For each hour, the angle made =

Therefore, when the hour hand moves from 12 to 5, the angle made =

** Answer: ** 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 =

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

(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 and 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 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 :

** 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) 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.

** Answer: **

- (a) True.
- (b) False.
- (c) True.
- (d) True.
- (e) True.

** Q3 ** Write down the measures of

(a) some acute angles.

(b) some obtuse angles.

(give at least two examples of each).

** Answer: **

- (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.

** Answer: **

- (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 =

** Answer: **

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.

** 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__.

** Answer: **

- (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 :

** Answer: ** 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 |

** Answer: **

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 |

## ** 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.

** Answer: **

PQ and XY intersect at A

Therefore

** Answer: ** 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

- (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.

- (i) AC = 3 - 1 = 2 units

** NCERT solutions for class 6 maths 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

(b) an obtuse-angled isosceles triangle

Isosceles traingle: Only two sides are of equal length

Obtuse angled : At least one angle greater than

** 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) with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
- (c) such that PQ = QR = PR = 5 cm.
- (d) with
- (e) with and XY = YZ.
- (f) with , and

** Answer: **

- (a) Scalene Triangle.
- (b) Scalene Triangle.
- (c) Equilateral Triangle.
- (d) Right-angled Triangle.
- (e) Right-angled 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 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 |

** 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.

## ** NCERT solutions for class 6 maths topic: Quadrilaterals **

** Answer: ** 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

** 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

**NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes Exercise 5.7**** **

- (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.

** Answer: **

- (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.

** 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.

** 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.

Make two more examples of each of these.

### ** Answer: **

(a) Quadrilateral

(b) Triangle

(c) Pentagon

(d) Octagon

### ** Answer: **

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

### ** Answer: **

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

### ** 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 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 : _______

** Answer: ** The number of

- Faces = (All triangular faces)
- Edges =
- Corners =

** Q4 ** A square pyramid has a square as its base.

- Faces : _______
- Edges : _______
- Corners : _______

** Answer: ** 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 : _______

** Answer: **

- Faces = (Two triangular faces and three square faces)
- Edges = 9
- Corners =

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

(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)

** Answer: T**he 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 **

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Chapter - 8 | |

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### ** NCERT Solutions for Class 6 - Subject wise **

** 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 and then refer to NCERT solutions for class 6.
- 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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