Important Questions for CBSE Class 6 Maths Chapter 5 - Understanding Elementary Shapes

Very Short Answer Questions                                                                                            1 Mark 

1. 1 mm = ____ cm 

Ans: 0.1 

2. Instrument used to measure angle is called_____. 

Ans: Protractor 

3. Standard unit for measuring an angle is called ______ and is denoted by ______. 

Ans: degree, $\circ$ 

4. ${90.5^\circ}$  is called ____ angle.

 Ans: Obtuse 

5. ${177^\circ}$  is called _____ angle. 

Ans: Obtuse 

6. The sum of angles of a quadrilateral is _______.

Ans: ${360^\circ}$ 

7. The diagonals of an isosceles trapezium are ______. 

Ans: Equal 

8. A sphere has _____ vertex and 0 edges. 

Ans: Zero 

9. Cube and cuboid have an equal number of faces, vertices and edges. Say True or False. 

Ans: True 

10. A triangular pyramid is called a ______. 

Ans: Tetrahedron

Short Answer Questions                                                                                                    2 Marks 

1. How many degrees are there in

(a) four right angles

Ans: four right angles $ = 4 \times {90^\circ } = {360^\circ }$.

(b) $2\dfrac{1}{2}$ right angles

$2\dfrac{1}{2}$ right angles $ = 2\dfrac{1}{2} \times {90^\circ }$

$ = \dfrac{5}{2} \times 90 = {225^\circ }$

2. How many degrees are there in between the clock hands when it displays ${7^\prime }0$ clock?

Ans: 

It is ${30^\circ }$between any two numbers on the clock.

So, there are 7 divisions between 12 and 7.

Thus, total degrees $ = 7 \times {30^\circ } = {210^\circ }$

3. What is the condition for two triangles to be congruent?

Ans: Two triangles are said to be congruent if the corresponding sides and angles of both triangles are equal to each other.

4. What is the perimeter of a triangle?

Ans: The sum of all three sides of a triangle is called the perimeter of a triangle.

5. Find the value of ${x^0}$.

Ans: Sum of angles of a triangle $ = {180^\circ }$(By angle sum property of a triangle)

${8^\circ } + {35^\circ } + {x^\circ } = {180^\circ }$

${43^\circ } + {x^\circ } = {180^\circ }$

${x^\circ } = {180^\circ } - {43^\circ }$

${x^\circ } = {137^\circ }$

6. Find angles of a triangle that are in ratio 4: 6: 8.

Ans: Let the angles be $4{x^0},6{x^0},8{x^0}$

$4x + 6x + 8x = {180^\circ }$ (Angle sum property of triangle)

$18x = {180^\circ }$

$x = {10^\circ }$

So, angles are ${40^\circ },{60^\circ },{80^\circ }$

7. Name the solid objects for each of the $3{\text{D}}$ shape

(a) cone

Ans: Party hats, oil funnel, Ice cream cone

(b) cylinder

Coke can, gas cylinder, electric cells

(c) cube 

Rubix, dice, sugar and ice cubes

Short Answer Questions                                                                                                    3 Marks

1. Explain the various types of triangles considering the length of their sides.

Ans: On the basis of the length of sides, there are three types of triangles:

(a) Equilateral triangle: It is a triangle in which all sides and all angles are equal to each other.

(b) Isosceles triangle: It is a triangle with two sides and two angles opposite to the two sides that are equal to each other.

(c) Scalene triangle: It has none of the sides or angles equal to each other.

2. Explain the types of triangles considering the angles.

Ans: On the basis of angles, there are three types of triangles:

(a). Acute angled triangle: Triangle in which all the three angles are acute (less than ${90^\circ }$)$\angle X,\angle Y,\angle Z < {90^\circ }$

(b). Right angled triangle: Triangle in which one angle is ${90^\circ }$, $\angle B = {90^\circ }$

(c) Obtuse angled triangle: Triangle in which at least one angle is obtuse(greater than ${90^\circ }$and less than ${180^\circ }$)

Long Answer Questions                                                                                                     4 Marks 

1. Say True or False

(a) Equilateral triangle, each angle measures ${60^0}$.

Ans: True

(b) A scalene triangle has two sides equal.

Ans: False, In a scalene triangle, none of the sides are equal.

(c) The angles opposite to equal sides of an Isosceles triangle are equal.

Ans: True

(d) In a right-angled triangle, the sum of two acute angles is ${180^\circ }$.

Ans: False, the sum of two acute angles is $ 90^\circ $

2. The measure of two angles of a triangle are ${72^0}$and ${55^0}$. Find the measure of the third angle. 

Ans: Let $\angle A,\angle B,\angle C$ are the angles of a triangle 

Let the required missing triangle be ${x^\circ }$

$\angle A + \angle B + \angle C = {180^\circ }$(By angle sum property of triangle)

Thus,

${72^\circ } + {55^\circ } + {x^\circ } = {180^\circ }$

${127^\circ } + {x^\circ } = {180^\circ }$

${x^\circ } = {180^\circ } - {127^\circ }$

${x^\circ } = {53^\circ }$

3. In $\Delta ABC$ if $3\angle A = 4\angle B = 5\angle C$. Calculate $\angle A,\angle B,\angle C$

Ans: let $3\angle A = 4\angle B = 5\angle C = {x^\circ }$

$3\angle A = {x^\circ }$, $4\angle B = {x^\circ }$and $5\angle C = {x^\circ }$

$ \Rightarrow \;\angle A = \dfrac{{{x^\circ }}}{3}\;\;,\;\;\angle B = \dfrac{{{x^\circ }}}{4}$ and $\angle C = \dfrac{{{x^\circ }}}{5}$

$\dfrac{{{x^\circ }}}{3} + \dfrac{{{x^\circ }}}{4} + \dfrac{{{x^\circ }}}{5} = {180^\circ }$   (by angle sum property of triangle)

${x^\circ }\left[ {\dfrac{1}{3} + \dfrac{1}{4} + \dfrac{1}{5}} \right] = {180^\circ }$

${x^\circ }\left[ {\dfrac{{20 + 15 + 12}}{{60}}} \right] = {180^2}$

${x^\circ }\left[ {\dfrac{{47}}{{60}}} \right] = 180$

${x^\circ } = \dfrac{{180 \times 60}}{{47}} = {229.78^\circ }$

So, $\angle A = \dfrac{{{x^\circ }}}{3} = {76.5^\circ },\;\angle B = \dfrac{{{x^\circ }}}{4} = {57.4^\circ },\;\angle C = \dfrac{{{x^\circ }}}{5} = {45.9^\circ }$

4. Explain the following:

(a) Convex quadrilateral

Ans: Quadrilateral which has each of the interior angles less than ${180^\circ }$ is called a convex quadrilateral.

(b) Concave quadrilateral

Ans: Quadrilateral which has each of the interior angles greater than ${180^\circ }$ is called a concave quadrilateral.

Long Answer Questions                                                                                                     5 Marks 

1. Define the following:

(a) Acute angle

Ans: Acute angle: Angle which is less than ${90^\circ }$ is called an acute angle

(b) Right angle

Ans: Right angle: Angle which is equal to ${90^\circ }$ is called a right triangle.

(c) Obtuse angle

Ans: Obtuse angle: Angle greater than ${90^\circ }$ and less than ${180^\circ }$ is called an obtuse angle.

(d) Straight angle

Ans: Straight angle: Angle equal to $180^\circ $ is called a straight angle.

(c) Complete angle

Ans: Complete angle: Angle equal to ${360^\circ }$ is called a complete angle.

(f) Zero angle 

Ans: Zero angle: Angle equal to ${0^\circ }$is called a zero angle.

2. State the type of angle

(a)  

Ans: Straight angle

(b)  

Ans: Right angle

(c)  

Ans: Obtuse angle

(d) 

Ans: Zero angle

(e)

Ans: Acute angle

(f)

Ans: Reflex angle

3. Explain the difference between Square and Rectangle.

Ans: 

Square	Rectangle
All sides are equal.	Only opposite sides are equal.

4. Explain the similarity between Rhombus and Parallelogram. 

Ans: 

• Both Rhombus and Parallelogram have two pairs of parallel sides.

• Both Rhombus and Parallelogram diagonals bisect each other.

     

Parallelogram                                                          Rhombus

5. Say True or False

(a) Parallelogram has both the diagonals equal.

Ans: True

(b) The diagonals of a rectangle are perpendicular to each other.

Ans: False

(c) A square is also a parallelogram.

Ans: True

(d) The diagonals of a rhombus are equal. 

Ans: True

6. Write the number of faces, edges and vertices of

(a) Square-based pyramid

Ans: Square based pyramid

Faces $ = 5$($4$ triangular, $1$ square)

Edges $ = 8$

Vertices $ = 1$

(b) Triangular based prism

Ans: Triangular based prism

Faces $ = 5$

Edges $ = 9$

Vertices $ = 6$

Class 6 Maths Chapter 5 Important Questions Free PDF Download

The Important Topics in Understanding Elementary Shapes Chapter Are as Follows:

• Line segments

• Angles and their types

• Measuring angles

• Perpendicular lines

• Classification of triangles

• Quadrilaterals

• Three-dimensional shapes

Chapter 5 - Understanding Elementary Shapes

Measuring Line segments

A line segment is a part of a line that includes any point on the line between its endpoints and is bounded by two distinct endpoints. Both endpoints are included in a closed line segment, while an open line segment removes both endpoints; exactly one of the endpoints is included in a half-open line segment.

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There Are Different Methods to Measure Line Segments

• Observing the line segments and comparing them.

• Tracing the line segments and comparing them.

• Measuring line segments by using a ruler and divider.

Angles

An angle is a figure created by two rays, called the angle's sides, which share a common endpoint, called the angle's vertex. In the plane, which contains the rays, angles created by two rays lie.

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Types of Angles

• Right Angle - When measured the angle is exactly 90 degrees.

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• Straight Angle - When measured the angle is exactly 180 degrees.

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• Acute Angle - When measured the angle is less than 90 degrees.

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• Obtuse Angle - When measured the angle is greater than 90 degrees but less than 180 degrees.

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• Reflex Angle - When measured the angle is greater than 180 degrees.

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Measuring Angles

An easy way to measure angles is by using a protractor. The steps of angle measurement are as follows:

• Place the protractor's midpoint at the angle of the vertex.

• Align one side of the angle with the protractor's zero axes.

• Read the degrees where the number scale is crossed by the other hand.

Perpendicular Lines

Perpendicular lines are described as two lines that at right angles meet or intersect with each other.

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Properties of Perpendicular Lines

• These lines always intersect at right angles i.e at 90 degrees.

• There are often opposite sides of a square and a rectangle perpendicular to each other.

• The sides of the right-angled triangle are perpendicular to each other, enclosing the right angle.

Triangles

A polygon with three sides and three vertices is a triangle. In geometry, it is one of the basic shapes.

Types of Triangles Based on Its Sides

• Scalene Triangle

A scale triangle is a triangle in which there are different lengths on all three sides. When the other two angles or the legs are not congruent, such right triangles can be a scalene triangle.

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• Isosceles Triangle

A triangle that has two sides of equal length is an isosceles triangle.

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• Equilateral Triangle

A triangle in which all three sides have the same length is an equilateral triangle.

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Types of Triangles Based on Its Angles

• Right-Angled Triangle

Right-angle is a triangle in which the angle between the two perpendicular lines in the triangle is 90 degrees i.e at a right angle. The basis for trigonometry is the relation between the sides and angles of a right-angle triangle. The hypotenuse is called the hand opposite the right angle.

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• Acute Angled Triangle

An acute-angled triangle is a triangle in which all three angles are acute i.e less than 90 degrees.

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• Obtuse Angled Triangle

An Obtuse angled triangle is a triangle in one of the angle is acute i.e greater than 90 degrees.

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Quadrilaterals

A quadrilateral is a polygon which has four edges and four vertices.

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The interior angles of quadrilaterals will always add up to 360 degrees.

Polygons

A polygon is a plane figure identified by a finite number of straight-line segments linked to form a polygonal chain or polygonal circuit that is closed. A polygon may be called the solid plane region, the bounding circuit, or the two together.

Types of Polygons

Polygon types are based on the number of sides which are as follows:

Three Dimensional Shapes

A three-dimensional shape can be described in geometry as a solid figure or an entity or shape that has length, width and height in three dimensions. Three-dimensional forms have thickness or width, unlike two-dimensional shapes.

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Few Basic Three-Dimensional Shapes Are 

• Cube

• Cuboid

• Pyramid

• Cone

• Prism

• Cylinder

• Sphere

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Importance of CBSE Class 6 Maths Chapter 5 Important Questions

The CBSE Class 6 Maths Chapter 5 is a detailed and important chapter that includes the concepts of shapes, angles, lines, and much more. From the chapter, students will be able to understand the different elementary shapes while improving their visualization. The chapter tells them how to look at different 3D-shaped objects and what are the different characteristics of these objects. To help them prepare the chapter in a better way, the experts at Vedantu have formulated the important questions for Class 6 Maths Chapter 5. These questions will help the students understand the chapter in a much better way.

In order to make sure that students are all prepared for their Maths exams, the experts at Vedantu have created these important questions. These will help them get top-notch solutions to challenging questions from the chapter. All the questions have been prepared according to CBSE guidelines. Students can solve the questions and get some practice before their final exams. The PDF file includes additional questions that might appear in the exams. These questions will help students understand the chapter properly and complete their revision in time.

Benefits of Class 6 Maths Chapter 5 Important Questions

• The important questions have been designed by the experts at Vedantu who are well-versed in the CBSE guidelines. After studying the question papers of previous years, they have compiled the questions that are most commonly asked in the exams.

• Every question has been solved using the right steps and the solutions have been explained in a step-by-step manner for the ease of understanding for the students.

• By downloading the important questions, students can understand the CBSE exam pattern and the types of questions that are common. Also, they can figure out the answering format in order to score good marks in the exams.

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Download Important Questions for CBSE Class 6 Maths Chapter 5

This is your chance to download Vedantu’s important questions for CBSE Class 6 Maths Chapter 5 and start your preparation in the best way. This is a very important topic for the students and needs to be thoroughly prepared for the exams. Download the important questions and practice to score good marks in the exams.

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