from a handpicked tutor in LIVE 1-to-1 classes

# If in Fig. 9.7, PQRS and EFRS are two parallelograms, then ar (MFR) = 1/2 ar (PQRS). Is the given statement true or false and justify your answer.

**Solution:**

We know that

PQRS and EFRS are on the same base SR and between the same parallels EF and SR

The areas will be equal

ar (PQRS) = ar (EFRS) …. (1)

ar (∆ MFR) = 1/2 ar (EFRS) …. (2)

From both the equations

ar (MFR) = 1/2 ar (PQRS)

Therefore, the statement is true.

**✦ Try This: **The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 5 cm and 4 cm is :

It is given that

Length of rectangle = 5 cm

Breadth of rectangle = 4 cm

Consider E, F, G and H as the mid-points of sides AB, BC, CD and AD

EFGH is a rhombus

Diagonals are EG and HF

So EF = BC = 5 cm

HF = AB = 4 cm

We know that

Area of rhombus = Product of diagonals/ 2

By further calculation

= (5 × 4)/2

= 20/2

= 10 cm²

Therefore, the figure obtained is a rhombus of area 10 cm².

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

**NCERT Exemplar Class 9 Maths Exercise 9.2 Sample Problem 2**

## If in Fig. 9.7, PQRS and EFRS are two parallelograms, then ar (MFR) = 1/2 ar (PQRS). Is the given statement true or false and justify your answer.

**Summary:**

The statement “If in Fig. 9.7, PQRS and EFRS are two parallelograms, then ar (MFR) = 1/2 ar (PQRS)” is true

**☛ Related Questions:**

- ABCD is a parallelogram and X is the mid-point of AB. If ar (AXCD) = 24 cm² , then ar (ABC) = 24 cm² . . . .
- PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS . . . .
- PQRS is a parallelogram whose area is 180 cm² and A is any point on the diagonal QS. The area of ∆ A . . . .

visual curriculum