# NCERT Class 9 Solutions: Areas of Parallelograms and Triangles (Chapter 9) Exercise 9.2 – Part 1 (For CBSE, ICSE, IAS, NET, NRA 2023)

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

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:

- 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