NCERT Class 9 Solutions: Areas of Parallelograms and Triangles (Chapter 9) Exercise 9.2 – Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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The Area of a Parallelogram It is Equal to the Product of th …

Q-1 In the figure, ABCD is a parallelogram, and . If , and , find .

Parallelomgram ABCD

Solution:

Given,

  • ABCD is a parallelogram, and
  • Also (opposite side of a parallelogram)
  • and

Now,

  • ()
  • (

Q-2 If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar

Solution:

Parallelogram ABCD
  • Given, E, F, G and H are respectively the mid-point of the sides of a parallelogram ABCD
  • To prove,
  • Construction, H and F are joined.

Proof,

  • and (opposite sides of a parallelogram) so
  • Also, and therefore and (H and F are mid points) Thus, ABFH and HFCD are parallelograms.
  • Now, And parallelogram ABFH lie on the same base FH and between the same parallel lines AB and HF.
  • So, area of … equation (1) (this is because area of triangle is and area of parallelogram is and the triangle and parallelogram share same base and height) ,
  • Similarly, area of … equation (2)

Adding equation (1) and (2)

  • Area of area of

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