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
- A plywood piece
- Graph paper
- Colour box
- Two wooden strips
- Cutter
- Adhesive
- Geometry box
Prerequisite Knowledge
- Area of a triangle.
- Area of a parallelogram.
Theory
- For area of triangle refer to Activity 21.
- For area of parallelogram refer to Activity 19.
Procedure
- Take a rectangular plywood piece of suitable size and by using adhesive, paste a graph paper on it.
- Take two wooden strips or wooden scale and fix these two horizontally so that they are parallel.
- 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) - Take any point T on the second strip and join it to P and Q. (see Fig. 22.1)
- T is any point on RS and PQ is parallel to RS.
- 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)
Demonstration
- 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.
- We can conclude that the area of the ΔTPQ is half of the area of parallelogram PQRS.
Observation
- The number of squares in ΔTPQ = ………….. ,
- 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
- deriving formula of the area of a triangle.
- 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.
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