CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

maths lab manual class 9 activities term 2

Verify the Algebraic Identity (a – b)³ = a³ – b³ – 3ab (a – b) Experiment Class 9 Maths Practical NCERT

The experiment to determine Verify the Algebraic Identity (a – b)³ = a³ – b³ – 3ab (a – b) are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 9 CBSE Verify the Algebraic Identity (a – b)³ = a³ – b³ – 3ab (a – b) Experiment

Determine Verify the Algebraic Identity (a – b)³ = a³ – b³ – 3ab (a – b) Class 9 Practical

OBJECTIVE

To verify the algebraic identity (a – b)³ = a³ – b³ – 3ab (a – b).

Materials Required

  1. Geometry box
  2. Acrylic sheet
  3. Scissors
  4. Adhesive/Adhesive tape
  5. Cutter

Prerequisite Knowledge

  1. Concept of cuboid and its volume.
  2. Concept of cube and its volume.

Theory

  1. For concept of cuboid and its volume refer to Activity 7.
  2. For concept of cube and its volume refer to Activity 7.

Procedure

  1. By using acrylic sheet and adhesive tape/adhesive, make a cube of side (a – b) units, where a > b. (see Fig. 8.1)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a - b)³ = a³ - b³ - 3ab (a - b) 1
  2. By using acrylic sheet and adhesive tape, make three cuboids each of dimensions, (a-b) x a x b. (see Fig. 8.2)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a - b)³ = a³ - b³ - 3ab (a - b) 2
  3. By using acrylic sheet and adhesive tape make a cube of side b units, (see Fig. 8.3)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a - b)³ = a³ - b³ - 3ab (a - b) 3
  4. Arrange all the cubes and cuboids as shown in Fig 8.4.
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a - b)³ = a³ - b³ - 3ab (a - b) 4

Demonstration
In Fig. 8.1, volume of the cube of side (a – b) units = (a – b)³
In Fig. 8.2, volume of a cuboid of sides (a – b) x a x b =(a – b)ab
In Fig. 8.2, volume of three cuboids = 3 x (a – b) ab In Fig. 8.3, volume of the cube of side b = b³
In Fig. 8.4, volume of the solid = Sum of volume of all cubes and cuboids
= (a- b)³ + (a – b) . ab + (a – b) . ab + (a – b) ab + b³
= (a – b)³+3 (a – b) . ab + b³ …(i)
Also, the obtained solid in Fig. 8.4 is a cube of side a.
Therefore, its volume = a³
From Eqs. (i) and (ii), we get
(a – b)³ + 3ab (a – b) + b³= a³
=> (a – b)³ = a³ – b³ – 3ab (a – b)
Here, volume is in cubic units.

Observation
By actual measurement,
a = …….. , b = …….. , a-b =…….. ,
So, a³ =…….. ,  ab = …….. ,
b³ =…….. ,  ab(a – b) = …….. ,
3ab(a – b) = …….. , (a – b)³ = ……..
Therefore, we observe that
(a-b)³ = a³ – b³ -3ab (a-b) or (a-b)³ =a³-3a²b + 3ab²-b³

Result
From above observation, algebraic identity for any a, to, where (a > b) is (a – b)³ = a³ – b³ – 3ab(a – b)
Has been verified geometrically by using cubes and cuboids.

Application
This identity is useful in

  1. many operations of algebraic expressions like as simplification and factorization.
  2. calculating cube of a number represented as the difference of two convenient numbers.

Viva Voce
Question 1:
What is the formula of the volume of a cube?
Answer:
Volume of a cube = side x side x side = ( side)³

Question 2:
What is the formula of the volume of a cuboid?
Answer:
Volume of a cuboid = length x breadth x height

Question 3:
How would you expand a³ – b³, in the terms of (a – b)³?
Answer:
We know that (a – b)³ = a³ – b³ – 3ab(a – b)
= a³ – b³ – 3a²b + 3ab² => a³ – b³ =(a – b)³ + 3a²b – 3ab²

Question 4:
What is the expanded form of (a – b)³?
Answer:
Expanded form of (a – b)³ = a³ -b³ – 3ab (a – b)

Question 5:
Does the resulted value of the product of (a – b)² and (a – b) is same as (a – b)³ ? Give reason.
Answer:
Yes, because (a – b)² (a – b) = (a – b)³ = a³ – b³ – 3ab (a – b) [∴ Am x An = (A)m+n]

Suggested Activity
Verify that (x – y)³ =x³ – 3x²y + 3xy² – y³ by taking x = 100 and y = 2.

Math LabsMath Labs with ActivityMath Lab ManualScience LabsScience Practical Skills

NCERT Class 9 Maths Lab Manual 

Find Probability of Unit’s Digit of Telephone Numbers Experiment Class 9 Maths Practical NCERT

The experiment to determine Find Probability of Unit’s Digit of Telephone Numbers are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 9 CBSE Find Probability of Unit’s Digit of Telephone Numbers Experiment

Determine Find Probability of Unit’s Digit of Telephone Numbers Class 9 Practical

Objective
To find experimental probability of unit’s digits of telephone numbers listed on a page selected at random of a telephone directory.

Materials Required

  1. Telephone directory
  2. Ruler
  3. Notebook
  4. Pen

Prerequisite Knowledge
Basic knowledge of probability.

Theory

  1. If E is an event that happen when an experiment is performed, then the experimental or empirical probability of the event E is given by
    P(E) = \(\frac { Number\quad oftrials\quad in\quad which\quad the\quad event\quad E\quad happened }{ Total\quad number\quad of\quad trials } =\frac { n(E) }{ n(S) }\)
    or
    Probability of an event E = P(E) = \(\frac { Number\quad of\quad trials\quad in\quad which\quad the\quad event\quad occurred }{ Total\quad number\quad of\quad trials }\)
  2. The probability of happening of an event always lies from 0 to 1, i.e. 0 ≤ P(E) ≤ 1.
    In percentage, it lies from 0% to 100%.
  3. If probability of an event say A is 1, i.e. P(A) = 1, then event A is called a certain event or sure event.
  4. If probability of an event say B is 0, i.e. P(B) = 0, then event B is called an impossible event.
  5. The sum of all the probabilities of all possible outcomes of an experiment is 1.

Procedure

  1. Taking a telephone directory, select any page at random.
  2. Suppose the count of total telephone numbers on the selected page is N.
  3. Unit place of any telephone number can be occupied by any one of the digits 0,1,2, ……. 9.
  4. Now, using tally marks, prepare a frequency distribution table for the digits at unit’s place.
  5. Now, using the table, write the frequency of each of the digits 0,1,2, …….. 9.
  6. By using the formula for experimental probability, find the probability of each digit.

Demonstration

1. Firstly, by using tally marks, prepare a frequency distribution table for the digits 0,1,2,…. 9

Digits 0 1 2 3 4 5 6 7 8 9
Tally marks frequency n0 n1 n2 n3 n4 n5 n6 n7 n8 n9

2. From the table, note down the frequency of each digit from 0 to 9.
3. We get that digits 0, 1,2,…, 9 are occurring n0, n1, n2, …, n9 times respectively.
4. Considering the occurrence of each digit as an event E, the probability of event E is
P(E) = \(\frac { Number\quad of\quad trials\quad in\quad which\quad event\quad occurred }{ Total\quad number\quad of\quad trials }\)
Hence, respective experimental probability of occurrence of 0, 1, 2, …, 9 is given by
P(0) = \(\frac { { n }_{ 0 } }{ N }\), P(1) = \(\frac { { n }_{ 1 } }{ N }\), ……., P(9) = \(\frac { { n }_{ 9 } }{ N }\)

Observations
Total telephone numbers on a page (N) = ………….
Number of times 0 occurring at unit’s place (n0) = …………..
Number of times 1 occurring at unit’s place (n1) = …………….
Number of times 2 occurring at unit’s place (n2) = …………..
Number of times 3 occurring at unit’s place (n3) = ………….
Number of times 4 occurring at unit’s place (n4) = ………….
……………..
……………….
Number of times 9 occurring at unit’s place (n9) = …………….
Hence, experimental probability of occurrence of 0 = P(0) = \(\frac { { n }_{ 0 } }{ N }\)
Now, experimental probability of occurrence of 1 = P(1) = \(\frac { { n }_{ 1 } }{ N }\)
P(2) = \(\frac { { n }_{ 2 } }{ N }\)
……….
……….
P(9) = \(\frac { { n }_{ 9 } }{ N }\)

Result
We have got the experimental probability of unit’s digits of telephone numbers listed on a page selected at random of a telephone directory.

Applications
The concept of experimental probability is useful in

  1. deciding premium tables by insurance companies. .
  2. stock market to forecast the performance of a company, by metreological department to forecast weather.

Viva-Voce

Question 1.
How will you define an event?
Answer:
An event for an experiment is the collection of some outcomes of the experiment.

Question 2.
How will you define the empirical probability P(E) of an event E?
Answer:
P(E) = \(\frac { Number\quad of\quad trials\quad in\quad which\quad E\quad has\quad happened }{ Total\quad number\quad of\quad trials }\)

Question 3.
What are the maximum and minimum values of the probability of an event?
Answer:
Maximum and minimum values of the probability of an event are 1 and 0 respectively.

Question 4.
What is the complement of an event E?
Answer:
1 – P(E)

Question 5.
What is the probability of a certain event?
Answer:
1

Question 6.
How many events can occur when a coin is tossed?
Answer:
Two events, i.e. head or tail.

Question 7.
How will you define a sure event?
Answer:
If probability of an event say A is 1, i.e. P(A) = 1, then event A is called a certain event or a sure event.

Question 8.
Is the sum of all the probabilities of all possible outcomes of an experiment 1?
Answer:
Yes, the sum of all the probabilities of all possible outcomes of an experiment is 1.

Suggested Activity
Find the experimental probability of getting a tail in tossing an unbiased coin 5,10,15,20,25,30 times.

Math LabsMath Labs with ActivityMath Lab ManualScience LabsScience Practical Skills

NCERT Class 9 Maths Lab Manual 

Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² Experiment Class 9 Maths Practical NCERT

The experiment to determine Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 9 CBSE Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² Experiment

Determine Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² Class 9 Practical

OBJECTIVE

To verify the algebraic identity (a+b)³ = a³+b³+ 3a²b + 3ab².

Materials Required

  1. Acrylic sheets
  2. Adhesive/Adhesive tape
  3. Scissors
  4. Geometry Box
  5. Cutter

Prerequisite Knowledge

  1. Concept of cuboid and its volume.
  2. Concept of cube and its volume.

Theory

  1. Cuboid A cuboid is a solid bounded by six rectangular plane surfaces, e.g. Match box, brick, box, etc., are cuboid, (see Fig. 7.1)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² 1
    Properties of cuboid are

    1. In a cuboid, there are 6 faces, 12 edges and 8 corners (four at bottom and four at top face) which are called vertices.
    2. Opposite faces of a cuboid are equal and parallel.
    3. The line segment joining the opposite vertices of cuboid is called the diagonal of a cuboid.
    4. There are four diagonals in a cuboid which are equal in length.
      Volume of cuboid = lbh
      where, l = length, b = breadth and h = height
  2. Cube A cuboid whose length, breadth and height are same, is called a cube, (see Fig. 7.2)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² 2
    Properties of cube are

    1. In a cube, there are 6 faces, 12 edges and 8 corners (four at bottom and four at top face) which are called vertices.
    2. All the six faces of a cube are congruent square faces.
    3. Each edge of a cube have same length.
      Volume of cube = a³
      where, a is side of cube.

Procedure

  1. Cut six squares of equal side a units from acrylic sheet. Paste all of them to form a cube by using adhesive tape/adhesive, (see Fig. 7.3)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² 3
  2. Cut six squares of equal side b units (b < a) from acrylic sheet. Paste all of them to form a cube by using adhesive tape/adhesive, (see Fig. 7.4)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² 4
  3. Also, cut 12 rectangles of length b units and breadth a units and 6 squares of side a units. Paste all of them to form a cuboid, (see Fig. 7.5)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² 5
  4. Cut 12 rectangles of length a units and breadth b units and 6 squares of side b units. Paste all of them to form a cuboid, (see Fig. 7.6)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² 6
  5. Arrange the cubes obtained in Fig 7.3 and Fig 7.4 and the cuboids obtained in Fig 7.5 and Fig 7.6 as shown in Fig 7.7
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² 7

Demonstration
For Fig. 7.3, volume of cube of side a units = a³
For Fig. 7.4, volume of cube of side b units = b³
For Fig. 7.5, volume of a cuboid of dimensions a x a x b units = a²b
So, volume of all three such cuboids = a²b + a²b + a²b = 3a²b
For Fig. 7.6, volume of a cuboid of dimensions a x b x b units = ab²
So, volume of all three such cuboids = ab² + ab² + ab² = 3ab²
In Fig. 7.7, we have obtained the cube of side (a + b) units.
So, volume of cube = (a + b)³
As, volume of cube of Fig. 7.7 = (Volume of cube of Fig. 7.3) + (Volume of cube of Fig. 7.4) + (Volume of three cuboids of Fig. 7.5) + (Volume of three cuboids of Fig. 7.6)
=> (a+b)³ = a³+b³+ 3a²b + 3ab²
Here, volume is in cubic units.

Observation
On actual measurement, we get
a =…….. , b = …….. ,
So, a³ =…….. , b³ = …….. ,
a2b = …….. , 3a²b = …….. ,
ab² = …….. , 3ab² = …….. ,
(a + b)³ = …….. ,
Hence, (a+b)³ = a³+b³+ 3a²b + 3ab²

Result
The algebraic identity (a+b)³ = a³+b³+ 3a²b + 3ab² has been verified.

Application
The identity is useful for

  1. calculating the cube of a number which can be expressed as the sum of two convenient numbers.
  2. simplification and factorization of algebraic expressions.

Viva Voce
Question 1:
Is (a + b)³ a trinomial?
Answer:
No, because (a + b)³ has four terms.

Question 2:
What is the degree of polynomial (x + 2y)³ ?
Answer:
3, because the highest power of variable in the expansion of (x + 2 y)³ will be 3.

Question 3:
In the identity of (a + b)³, what do you mean by a³ and 3a²b?
Answer:
a³ means volume of cube of side a and 3a²b means volume of three cuboids of dimensions a, a and b.

Question 4:
What is the maximum number of zeroes that a cubic polynomial can have?
Answer:
Three

Question 5:
What is the expanded form of (a + b)³ ?
Answer:
(a+b)³ = a³+b³+ 3a²b + 3ab²

Question 6:
For evaluating (101)³, which formula we should use?
Answer:
We should use (a+b)³ = a³+b³+ 3a²b + 3ab² by taking a = 100 and b = 1

Suggested Activity
Verify that (a+b)³ = a³+b³+ 3a²b + 3ab² by taking x = 11 units, y- 3 units.

Math LabsMath Labs with ActivityMath Lab ManualScience LabsScience Practical Skills

NCERT Class 9 Maths Lab Manual 

Verify that in a Triangle, Longer Side has the Greater Angle Experiment Class 9 Maths Practical NCERT

The experiment to determine Verify that in a Triangle, Longer Side has the Greater Angle are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 9 CBSE Verify that in a Triangle, Longer Side has the Greater Angle Experiment

Determine Verify that in a Triangle, Longer Side has the Greater Angle Class 9 Practical

OBJECTIVE

To verify experimentally that in a triangle, the longer side has the greater angle opposite to it.

Materials Required

  1. Cardboard
  2. Coloured glazed papers
  3. White paper
  4. Tracing paper
  5. Scissors
  6. Geometry box
  7. Sketch pens
  8. Adhesive

Prerequisite Knowledge
Concept of triangle and its properties.

Theory
For concept of triangle and its properties refer to Activity 12.

Procedure

  1. Take a cardboard of suitable size and by using adhesive, paste a white paper on it.
  2. Cut out a ΔABC from a glazed paper and by using adhesive, paste it on cardboard, (see Fig. 15.1)
    NCERT Class 9 Maths Lab Manual - Verify that in a Triangle, Longer Side has the Greater Angle 1
  3. Measure the lengths of all the three sides of ΔABC and identify that which of them is longest.
  4. All the three angles of a triangle are to be marked, (see Fig. 15.2)
    NCERT Class 9 Maths Lab Manual - Verify that in a Triangle, Longer Side has the Greater Angle 2
  5. Using a tracing paper, make the cut out of the angle opposite to the longest side SC, i.e. ∠A. (see Fig. 15.3)
    NCERT Class 9 Maths Lab Manual - Verify that in a Triangle, Longer Side has the Greater Angle 3
  6. Compare the cut out of the angle with remaining angles. (see Fig. 15.4)
    NCERT Class 9 Maths Lab Manual - Verify that in a Triangle, Longer Side has the Greater Angle 4

Demonstration
We came to know that ∠A > ∠B and ∠A > ∠C , BC > AC,
So, we get since ∠A > ∠B
Also, BC > AB, since ∠A > ∠C
Thus, we observe that the angle belongs to longer side is greater than the angle opposite to other side.

Observation
Length of side AB = ……….. , Length of side BC = ………. , Length of side CA = ………… ,
Measure of the angle opposite to the longest side = …………. ,
Measure of the other two angles = …………… and ………. ,
The angle opposite to the …………. side ……….. is than either of the other two angles.

Result
We have verified experimentally that in a triangle, the longest side has the greater angle opposite to it.

Application
The result can be useful in different geometrical problems.

Viva Voce
Question 1:
In the right angled triangle, which one is the longest side?
Answer:
Hypotenuse

Question 2:
Does sum of any two sides of a triangle is always smaller than the third side?
Answer:
No, because the sum of any two sides of a triangle is always greater than the third side.

Question 3:
Is it possible to draw a triangle having sides 7 cm, 3 cm and 10 cm?
Answer:
No, because the sum of any two sides of a triangle is always greater than the third side.

Question 4:
Which type of triangle, have any two sides equal?
Answer:
Isosceles triangle

Question 5:
Which type of triangle, have all sides equal?
Answer:
Equilateral triangle

Question 6:
Does the longer side has the smaller angle opposite to it in a triangle?
Answer:
No, the longer side has the greater angle opposite to it in a triangle.

Question 7:
If in ΔABC, ∠A > ∠B, then what can you say about the opposite sides of ∠A and ∠B?
Answer:
BC > AC, because ∠A is greater than ∠B, so side opposite to ∠A will also be greater than the side opposite to ∠B.

Question 8:
Which type of triangle, have all sides unequal?
Answer:
Scalene triangle

Suggested Activity
Verify experimentally the relation between unequal sides of a triangle and the angles opposite to them.

Math LabsMath Labs with ActivityMath Lab ManualScience LabsScience Practical Skills

NCERT Class 9 Maths Lab Manual 

Verify that the Ratio of the Areas of a Parallelogram Experiment Class 9 Maths Practical NCERT

The experiment to determine Verify that the Ratio of the Areas of a Parallelogram are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 9 CBSE Verify that the Ratio of the Areas of a Parallelogram Experiment

Determine Verify that the Ratio of the Areas of a Parallelogram Class 9 Practical

OBJECTIVE

To verify that the ratio of the areas of a parallelogram and a triangle on the same base and between the same parallels is 2 : 1.

Materials Required

  1. A plywood piece
  2. Graph paper
  3. Colour box
  4. Two wooden strips
  5. Cutter
  6. Adhesive
  7. Geometry box

Prerequisite Knowledge

  1. Area of a triangle.
  2. Area of a parallelogram.

Theory

  1. For area of triangle refer to Activity 21.
  2. For area of parallelogram refer to Activity 19.

Procedure

  1. Take a rectangular plywood piece of suitable size and by using adhesive, paste a graph paper on it.
  2. Take two wooden strips or wooden scale and fix these two horizontally so that they are parallel.
  3. Fix a pair of points P and Q on the base strip and take a pair of points R and S on the another
    strip such that PQ = PS. (see Fig. 22.1)
  4. Take any point T on the second strip and join it to P and Q. (see Fig. 22.1)
    NCERT Class 9 Maths Lab Manual - Verify that the Ratio of the Areas of a Parallelogram 1
  5. T is any point on RS and PQ is parallel to RS.
  6. We find that ΔTPQ and parallelogram PQRS lie on the same base PQ and between the same parallels, (see Fig. 22.1)
    Note:
    We may take different triangles TPQ by taking different positions of point T and the two parallel strips, (see Fig. 22.2)
    NCERT Class 9 Maths Lab Manual - Verify that the Ratio of the Areas of a Parallelogram 2

Demonstration

  1. Count the number of squares contained in each of the above ΔTPQ and parallelogram PQRS, keeping half square as ½ and more than half square as 1, leaving those squares which are less than half square.
  2. We can conclude that the area of the ΔTPQ is half of the area of parallelogram PQRS.

Observation

  1. The number of squares in ΔTPQ = ………….. ,
  2. The number of squares in parallelogram PQRS = …………. ,
    Then, the area of parallelogram PQRS = 2 (area of ΔTPQ).
    Hence, area of parallelogram PQRS : area of ΔTPQ = …………. ,

Result
We find that the ratio of the area of a parallelogram and the area of a triangle on the same base and between the same parallels is 2 : 1.

Application
This activity can be used in

  1. deriving formula of the area of a triangle.
  2. solving some problems of mensuration.

Viva Voce
Question 1:
If a triangle and a parallelogram are on the same base and between the same parallels, then how can we relate the area of triangle and parallelogram?
Answer:
Area of the triangle is half the area of parallelogram.

Question 2:
If a triangle and a parallelogram are on the same base and having the equal area, then will they have same altitudes?
Answer:
No, they will not have same altitudes.

Question 3:
If a triangle and a parallelogram are on the same base and between same parallels, then what would be ratio of the area of the triangle to area of parallelogram?
Answer:
Required ratio = 1:2

Question 4:
Do we obtain a parallelogram and a triangle, whose area are in ratio 2:1?
Answer:
Yes, when a parallelogram and a triangle should be on the same base and between same parallels.

Question 5:
How can we find the area of a parallelogram with the help of a triangle?
Answer:
Area of a parallelogram = 2 x Area of a triangle
( which made by one of the diagonal of parallelogram)

Question 6:
How can we find the altitude of a parallelogram?
Answer:
Altitude of a parallelogram is the perpendicular drawn from one line to the another parallel line.

Question 7:
A triangle and a parallelogram on the same base and between the same parallels, will have same altitudes?
Answer:
Yes, they will have same altitudes because distance between two parallel lines remain same at all the points.

Suggested Activity
To verify experimentally the relationship between the areas of a parallelogram and a triangle on the same base and between the same parallels by cut out method.

Math LabsMath Labs with ActivityMath Lab ManualScience LabsScience Practical Skills

NCERT Class 9 Maths Lab Manual