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NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes provided here. 6 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.
Download - NCERT Books for Class 6
Straight angle = 180 degrees and right angle = 90 degrees.
Acute angle: When an angle is smaller than a right angle, we call it an acute angle.
Obtuse angle: When an angle is bigger than a right angle but smaller than a straight angle, we call it an obtuse angle.
Reflex angle: When an angle is larger than a straight angle, we call it a reflex angle.
Sum of interior angles of a triangle=180 degree
Sum of all interior angles of a polygon with n side=(n - 2)180 degrees
Based on | Triangle Name | Description |
Sides | Scalene triangle | All three sides are unequal. |
Isosceles triangle | Any two sides are equal. | |
Equilateral triangle | All three sides are equal. | |
Angles | Acute angled triangle | All the angles are acute. |
Right-angled triangle | Anyone's angle is the right angle. | |
Obtuse angled triangle | Anyone's angle is obtuse. |
Quadrilateral Type | Property |
Rhombus | All four sides are of equal length. |
Square | It is a rhombus with four right angles. |
Parallelogram | It has two pairs of parallel sides. |
Rectangle | It is a parallelogram with four right angles. |
Trapezium | It has one pair of parallel sides. |
Polygon Name | No. of Sides |
Triangle | 3 |
Quadrilateral | 4 |
Pentagon | 5 |
Hexagon | 6 |
Heptagon | 7 |
Octagon | 8 |
Nonagon | 9 |
Decagon | 10 |
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.
[Note : If A,B,C are any three points on a line such that AC + CB = AB, then we can be sure that C lies between A and B.]
Answer:
Yes
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.
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:
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
Answer:
Q3 Write down the measures of
(a) some acute angles.
(b) some obtuse angles.
(give at least two examples of each).
Answer:
Q4 Measure the angles given below using the Protractor and write down the measure.
Answer:
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 :
Answer:
Answer:
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
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 :
Answer:
Answer:
PQ and XY intersect at A
Therefore
Answer: The angles of the two set squares are
(i) 90o, 60o and 30o
(ii) 90o, 45 o, and 45o
Yes they have the common angle measure 90 o
Q4 Study the diagram. The line is perpendicular to line
Answer:
NCERT Solutions for Class 6 Maths Topic: Classification of Triangles
Q1 Try to draw rough sketches of
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 :
Answer:
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:
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.
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
Answer:
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?
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.
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.
Answer:
Q3 A triangular pyramid has a triangle as its base. It is also known as a tetrahedron.
Answer: The number of
Q4 A square pyramid has a square as its base.
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.
Answer:
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: The shape of the following things are
Understanding Elementary Shape Class 6 Maths Chapter 5-Summary
In Class 6 Maths Chapter 5, "Understanding Elementary Shapes," the following topics are covered:
Measuring Line Segment: This topic focuses on measuring the length of a line segment using a ruler or a measuring scale. Students learn how to read measurements in centimeters (cm) and millimeters (mm) and understand the concept of units of length.
Angles - 'Right' and 'Straight': Students are introduced to angles and learn about two specific types: right angles and straight angles. A right angle measures exactly 90 degrees and forms the shape of an "L." A straight angle measures exactly 180 degrees and forms a straight line.
Angles - 'Acute', 'Obtuse', and 'Reflex': This topic expands on angles by introducing acute angles, which are less than 90 degrees, and obtuse angles, which are greater than 90 degrees but less than 180 degrees. Students also learn about reflex angles, which measure greater than 180 degrees but less than 360 degrees.
Measuring Angles: Students explore how to measure and draw angles using a protractor. They understand that the measure of an angle is represented in degrees and learn how to determine the measurement of an angle accurately.
Perpendicular Line: This topic introduces the concept of perpendicular lines. Students learn that perpendicular lines are two lines that intersect at a right angle, forming four right angles at the point of intersection.
Classification of Triangles: Students learn about the classification of triangles based on their sides and angles. They study equilateral triangles (all sides and angles are equal), isosceles triangles (two sides and two angles are equal), and scalene triangles (all sides and angles are different).
Quadrilaterals: This topic focuses on quadrilaterals, which are polygons with four sides. Students learn about different types of quadrilaterals, such as squares, rectangles, parallelograms, and trapezoids. They understand the properties and characteristics of each type.
Polygons: Students delve into the concept of polygons in general, which are closed figures formed by line segments. They explore the properties of polygons and study various types, including triangles, quadrilaterals, pentagons, hexagons, and so on.
Three-Dimensional Shape: This topic introduces three-dimensional shapes, also known as solid shapes. Students learn about common three-dimensional shapes like cubes, cuboids, cylinders, cones, and spheres. They understand the distinguishing features and characteristics of each shape.
Also Check -
NCERT Books and NCERT Syllabus
Chapters No. | Chapters Name |
Chapter - 1 | |
Chapter - 2 | |
Chapter - 3 | |
Chapter - 4 | |
Chapter - 5 | Understanding Elementary Shapes |
Chapter - 6 | |
Chapter - 7 | |
Chapter - 8 | |
Chapter - 9 | |
Chapter -10 | |
Chapter -11 | |
Chapter -12 | |
Chapter -13 | |
Chapter -14 |
Keep learning and working hard!
A triangular prism has six corners, also known as vertices. In a triangular prism, there are three vertices at the top triangle and three vertices at the bottom triangle. These vertices are connected by edges to form the prism.
In a rectangle, each angle measures 90 degrees. A rectangle is a quadrilateral with four right angles (90-degree angles). The opposite sides of a rectangle are parallel, and all four angles are equal, measuring 90 degrees each. This property of rectangles makes them useful for various geometric and architectural applications. Students can study understanding elementary shapes class 6 pdf after downloading form the website.
If a triangle has three equal sides, it is called an equilateral triangle. In an equilateral triangle, all three angles are equal. Since the sum of angles in any triangle is always 180 degrees, each angle of an equilateral triangle measures 60 degrees. Also these concepts are discussed in class 6 maths chapter 5 pdf which can be downloaded from careers360 website.
There are 9 exercise solved in the maths class 6 chapter 5 Understanding Elementary Shapes.
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