Page 58 - Mathematics Class - IX

4. Take any point T on the second strip and join it to P and Q (Fig. (a)).

5. T is any point on RS and PQ is parallel to RS.

6. We find that ∆TPQ and parallelogram PQRS lie on the same base PQ and between the same parallels
(Fig. (a)).

7. Count the number of squares contained in each of the above ∆TPQ and parallelogram PQRS, keeping half

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square as and more than half as 1 and leaving those squares which contain less than half square.
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8. We can conclude that the area of the ∆TPQ is half of the area of parallelogram PQRS.

OBSERVATIONS

1. The number of squares in ∆TPQ =...............

2. The number of squares in parallelogram PQRS =............... .

Then, the area of parallelogram PQRS = 2 (area of ∆TPQ).

Hence, area of parallelogram PQRS : area of ∆TPQ = ........ : ...........

INFERENCE

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

EXTENDED TASK

1. 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.

2. Identify a field in your surroundings and measure its area.

APPLICATION

This activity can be used in

1. Deriving formula of the area of a triangle.

2. Solving some problems of mensuration.

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