Question

If X and Y are the centres of two identical circles of radius 7 cm and AB = 3 cm, what is the area of the rectangle PQRS (in cm2)?

1) 196
2) 392
3) 154
4) 350

Answer 1

The area of rectangle PQRS is 350 cm².

Option (4) is correct.

Given:

• If X and Y are the centres of two identical circles of radius 7 cm.
• AB = 3 cm

To find: what is the area of the rectangle PQRS (in cm2)?

1) 196

2) 392

3) 154

4) 350

Solution:

Area of rectangle= length×breadth

Step 1:

Find breadth of the rectangle.

As it is clear that breadth of rectangle is Diameter of circle.

From attached figure, it is shown that QR=CD

CD= Diameter

So,

Breadth (QR)= 14 cm

Step 2:

Find length of the rectangle.

As it is clear that length of rectangle can be calculated using

EF=EB+AF-AB

(because AB is considered twice while taking length of EF)

PQ=EF

length(EF) = 2Diameter- length of AB

length= $2 \times 14 - 3$

length(PQ)$= 25 \: cm$

Step 3:

Area of PQRS= PQ×QR

Area of PQRS$\bf =25 \times 14$

Thus,

Area of PQRS= 350 cm².

Option (4) is correct.

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