**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**

- Area of parallelogram = base x height.
- 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**

- Draw a parallelogram by paper folding activity.
- Cut this parallelogram using scissors and name it as ABCD, [fig.(i)].

- Mark any point E on DC.
- 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)].

- Cut the parallelogram ABCD along AE to get ∆AED.
- Paste the ∆AED on the other side along BC of parallelogram ABCD as shown in fig. (iii).

- We get new parallelogram AEPB.

**Observation**

- We observe that the two parallelograms ABCD and ABPE have same base AB.
- 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**

- This theorem can be proved by using a graph paper. Students will try this and verify the theorem.
- 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 cm^{2}.

What will be the area of second square ?

**Answer:**

64 cm^{2}

**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 cm^{2}

(ii) 64 cm^{2}

(iii) 36 cm^{2}

(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 cm^{2}, then ar(∆BEF) is

(i) 80 cm^{2}

(ii) 160 cm^{2}

(iii) 40 cm^{2}

(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 cm^{2}

(ii) 384 cm^{2}

(iii) 24 cm^{2}

(iv) none of these

**Question 7.**

Calculate the area of a trapezium PQRS:

(i) 64 cm^{2}

(ii) 156 cm^{2}

(iii) 180 cm^{2}

(iv) none of these

**Question 8.**

Areas of two parallelograms ABCD and PQRS are equal 20 cm^{2}. 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 cm^{2}, find ar (||gm ABCD):

(i) 60 cm^{2}

(ii) 160 cm^{2}

(iii) 80 cm^{2}

(iv) none of these

**Answers**

- (i)
- (i)
- (ii)
- (i)
- (ii)
- (i)
- (iii)
- (i)
- (iii)

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