CBSE Class 9 Maths Lab Manual – Area of Parallelograms on the Same Base

CBSE Class 9 Maths Lab Manual – Area of Parallelograms on the Same Base and between the Same Parallels

Objective
To show that the parallelograms on the same base and between the same parallel lines are equal in area by paper cutting and pasting.

Prerequisite Knowledge

1. Area of parallelogram = base x height.
2. Shortest distance between two parallel lines is the perpendicular distance between parallel lines and it remains same for that pair of parallel lines.

Materials Required
Glazed paper, a pair of scissors, gluestick, geometry box.

Procedure

1. Draw a parallelogram by paper folding activity.
2. Cut this parallelogram using scissors and name it as ABCD, [fig.(i)].
   
3. Mark any point E on DC.
4. From A fold the parallelogram till the point E (any point on DC). A crease AE is formed, fill another colour in ∆ADE. [fig. (ii)].
   
5. Cut the parallelogram ABCD along AE to get ∆AED.
6. Paste the ∆AED on the other side along BC of parallelogram ABCD as shown in fig. (iii).
   
7. We get new parallelogram AEPB.

Observation

1. We observe that the two parallelograms ABCD and ABPE have same base AB.
2. Two parallelograms lie between same parallel lines, i.e., AB and CD and height between them is same at all points.
   By formula, area of parallelogram = base x height
   ar(||gm ABCD) = AB x EH
   ar(||gm ABPE) = AB x EH

Result
We have verified that two parallelograms lying on same base and between same parallel lines are equal in area.

Learning Outcome
Students follow that the parallelograms on the same base and between the same parallels have same area.

Activity Time

1. This theorem can be proved by using a graph paper. Students will try this and verify the theorem.
2. Prove that areas of a rectangle and a square of same height and on the same base are equal by using paper cutting and pasting method.

Viva Voce

Question 1.
How many kinds of parallelogram are possible ?
Answer:
3 main kinds (rectangle, square, rhombus).

Question 2.
What is the altitude of a parallelogram ?
Answer:
Altitude of a parallellogram is a perpendicular distance between the vertex to its opposite side.

Question 3.
If the two squares are lying on the same base and between the same parallel lines and area of the one square is 64 cm².
What will be the area of second square ?
Answer:
64 cm²

Question 4.
Two squares are lying on the same base and having same height and area of one of square is 121 cm . What will be the side of another square ?
Answer:
11cm.

Question 5.
In a triangle, a median divides it into two triangles. What will be ratio of areas of two small triangles so formed ?
Answer:
Areas of two triangles will be same.

Multiple Choice Questions

Question 1.
A parallelogram ABCD and a rectangle ABPQ are on the same base AB and between the same parallels AB and CQ. If AB = 8 cm and AQ = 6 cm, find the area of parallelogram ABCD:
(i) 48 cm²
(ii) 64 cm²
(iii) 36 cm²
(iv) none of these

Question 2.
ABCD is a parallelogram. If AB = 8 cm, altitude DM = 6 cm and altitude DN = 4.8 cm, find the perimeter of parallelogram ABCD:

(i) 36 cm
(ii) 10.8 cm
(iii) 14 cm
(iv) none of these

Question 3.
ABCD is a parallelogram, in which AB ⊥DE and CF ⊥ AD. If AB = 16 cm, DE = 8 cm and CF = 10 cm, find AD:
(i) 12 cm
(ii) 12.8 cm
(iii) 128 cm
(iv) none of these

Question 4.
In the given figure, if ar(||gm ABCD) = 80 cm², then ar(∆BEF) is

(i) 80 cm²
(ii) 160 cm²
(iii) 40 cm²
(iv) none of these

Question 5.
PQRS and ABRS are parallelograms and X is any point on the side BR. What is the ratio of ar(∆AXS) and ar(PQRS)?
(i) 2:1
(ii) 1:2
(iii) 3:2
(iv) none of these

Question 6.
Find the area of a rhombus, if the lengths of its diagonals are 16cm and 24cm respectively:
(i) 192 cm²
(ii) 384 cm²
(iii) 24 cm²
(iv) none of these

Question 7.
Calculate the area of a trapezium PQRS:

(i) 64 cm²
(ii) 156 cm²
(iii) 180 cm²
(iv) none of these

Question 8.
Areas of two parallelograms ABCD and PQRS are equal 20 cm². Are these two parallelograms congruent?

(i) no
(ii) yes
(iii) can’t say
(iv) none of these

Question 9.
ABCD is a parallelogram and P is any point on the side CD. If ar(∆BAP) = 40 cm², find ar (||gm ABCD):
(i) 60 cm²
(ii) 160 cm²
(iii) 80 cm²
(iv) none of these

Answers

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

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