The figure below illustrates that area of triangle is ½ that of a parallelogram, if they are between same parallel lines and have same base.

Q-5 In the figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that

Solution (i):

Parallelogram PQRS and ABRS are on the same base SR

And, SR and PB are the same parallel lines. Therefore they have the same base length and height. Thus,

…………equation (1)

Solution (ii):

In triangle and parallelogram ABRS are on the same base AS

And, AS and BR are the same parallel lines.

……………..equation (2)

From (1) and (2),

Q-6 A farmer was having a field in the form of a parallelogram ABCD. She took any point P on CD and joined it to points A and B. In how many parts the fields is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?

Solution:

The field is divided into three parts.

The three parts triangles, namely, .

Area of …………..equation (1)

Since, triangle and parallelogram on the same base, area of

From (1) and (2),

Area of

Area of

Area of

Area of ………equation (3)

Now form half the area of ABCD and form the other half, therefore, the farmer should sow wheat in one of these half and pulses in other half.