# 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)