# NCERT Class 9 Solutions: Areas of Parallelograms and Triangles (Chapter 9) Exercise 9.2 – Part 1

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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