NCERT Class 9 Solutions: Areas of Parallelograms and Triangles (Chapter 9) Exercise 9.2 – Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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

Area of Triangle

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

Parallelogram PQRS and ABRS

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 are 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:

Parallelogram ABCD
  • 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.

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