# PQRS is a parallelogram whose area is 180 cm² and A is any point on the diagonal QS. The area of ∆ ASR = 90 cm². Is the given statement true or false and justify your answer.

**Solution:**

It is given that

PQRS is a parallelogram whose area is 180 cm²

A is any point on the diagonal QS

area of ∆ ASR = 90 cm²

We know that a diagonal divides it into two triangles of equal areas

So ar (∆ ASR) < ar (∆ SRQ)

Therefore, the statement is false.

**✦ Try This: **PQRS is a parallelogram whose area is 120 cm² and A is any point on the diagonal QS. Find the area of ∆ ASR.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 9

**NCERT Exemplar Class 9 Maths Exercise 9.2 Problem 3**

## PQRS is a parallelogram whose area is 180 cm² and A is any point on the diagonal QS. The area of ∆ ASR = 90 cm². Is the given statement true or false and justify your answer.

**Summary:**

The statement “PQRS is a parallelogram whose area is 180 cm² and A is any point on the diagonal QS. The area of ∆ ASR = 90 cm²” is false

**☛ Related Questions:**

- ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then ar (BDE) = 1/4 ar . . . .
- In Fig. 9.8, ABCD and EFGD are two parallelograms and G is the mid-point of CD. Then ar (DPC) = 1/2 . . . .
- PQRS is a square. T and U are respectively, the mid-points of PS and QR (Fig. 9.9). Find the area of . . . .

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