CBSE Class 9 Maths Lab Manual – Area of a Parallelogram

CBSE Class 9 Maths Lab Manual – Area of a Parallelogram

Objective
To show that the area of a parallelogram is equal to the product of its base and corresponding height by using paper cutting and pasting.

Prerequisite Knowledge

1. Construction of parallelogram by paper folding.
2. Area of rectangle = length x breadth
3. Area of parallelogram = base x corresponding height.

Materials Required
Glazed papers, pencil, a pair of scissors, gluestick.

Procedure

1. Draw a parallelogram by paper folding using coloured glazed paper and name it as ABCD.
2. Cut the parallelogram with the help of scissors.
3. In the parallelogram, draw a perpendicular from a vertex D to its opposite side AB of the parallelogram ABCD by paper folding.
4. We will get a crease along DE. Dark the colour in AADE [fig (i)]. Now cut it along DE. We will get two pieces, one triangle named as AED and other one a trapezium named E’D’CB as shown in fig.(ii).
   
   
5. Paste this triangular piece AED on the other side of trapezium such that its side AD coincides with BC [fig (iii)].
   
6. After pasting, we get a rectangle E’ECD’ with length as E’B + BE = E’E = D’C = AB and breadth as E’D’ = EC.

Observation
We observe that new figure D’E’EC is a rectangle.
Area of parallelogram ABCD = Area of rectangle E’ECD’
= length x breadth
= E’E x D’E’
= AB x DE
Hence, Area of parallelogram = Base x Height

Result
It is verified that the area of a parallelogram is equal to the product of its base and corresponding height by paper cutting and pasting method.

Learning Outcome
We can draw perpendicular from different vertices on opposite sides of parallelogram and verify that the area of the parallelogram is the product of base and height.
Area of parallelogram with the same base and the same height are identical. This leads to famous theorem:
“Parallelogram between the same parallel lines and on the same base are equal in area.”

Activity Time
Verify the area of a parallelogram is equal to the product of its base and corresponding height in which perpendicular falls outside the base of the parallelogram.

Viva Voce

Question 1.
What is the relation between the area of a triangle and area of a parallelogram, if they lie on the same base and between the same parallel lines?
Answer:
Area of parallelogram is twice the area of triangle.

Question 2.
What is the area of a parallelogram and area of a triangle ?
Answer:
Area of a triangle = \(\frac{ 1 }{ 2 }\) x base x height.
Area of a parallelogram = base x height.

Question 3.
A ∆ABC and a parallelogram ABCD are on the same base AB and their height is also same. If the area of the triangle is 21 cm², what would be the area of the parallelogram ?
Answer:
42 cm².

Question 4.
If one rectangle and one parallelogram lying on the same base and between the same parallel lines then what will be area of the rectangle ?
Answer:
ar(rectangle) = ar (parallelogram)

Question 5.
In a parallelogram ABCD, AB = 7.2 cm and altitudes corresponding to sides AB and AD are respectively 10cm and 8cm. Find AD.
Answer:
9cm

Multiple Choice Questions

Question 1.
What will be the area of a parallelogram if its one of sides is 12 cm and its corresponding height is 6 cm?
(i) 72cm²
(ii) 24 cm²
(iii) 36 cm²
(iv) none of these

Question 2.
ABCD is a parallelogram in which AB = 9.5 cm and its perimeter is 30 cm. The length of CB will be:
(i) 9.5 cm
(ii) 5.5 cm
(iii) 15 cm
(iv) none of these

Question 3.
‘RENT’ is a parallelogram, in which RE = 4 cm and EN = 6 cm. TR will be:
(i) 6 cm
(ii) 4 cm
(iii) 10 cm
(iv) none of these

Question 4.
In a parallelogram ABCD, if AB = 12 cm and BC = 6 cm, then CD will be:
(i) 12 cm
(ii) 3 cm
(iii) 6 cm
(iv) none of these

Question 5.
In a parallelogram PQRS, SR = 7 cm, its corresponding altitude = 6 cm and QR = 8 cm. Find its corresponding altitude to PS:

(i) \(\frac{ 21 }{ 4 }\) cm
(ii) 5.7 cm
(iii) \(\frac{ 6 }{ 8 }\) cm
(iv) none of these

Question 6.
If a parallelogram is a square of side 7 cm, then what will be its area ?
(i) 49 cm²
(ii) 14 cm²
(iii) 3.5 cm²
(iv) none of these

Question 7.
If a parallelogram is a rectangle of sides 7 cm and 8 cm, then what will be the area of parallelogram ?
(i) 16 cm²
(ii) 24 cm²
(iii) 56 cm²
(iv) none of these

Question 8.
If a parallelogram is in the shape of a rhombus having diagonals 12 cm and 14 cm, what will be the area of parallelogram ?
(i) 21cm²
(ii) 168 cm²
(iii) 84 cm²
(iv) none of these

Question 9.
Is a trapezium a parallelogram ?
(i) yes
(ii) no
(iii) can’t say
(iv) none of these

Answers

1. (i)
2. (ii)
3. (i)
4. (i)
5. (i)
6. (i)
7. (iii)
8. (iii)
9. (ii)

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