# Class 7 Maths Chapter 11 Exercise 11.4 Pdf Notes NCERT Solutions

Class 7 Maths Chapter 11 Perimeter And Area Exercise 11.4 pdf notes:-

- Exercise 11.1
- Exercise 11.2
- Exercise 11.3

**Exercise 11.4** Class 7 maths Chapter 11 Pdf Notes:-

**To see video Solution Of This Exercise Click Here**

## Ncert Solution for Class 7 Maths Chapter 11 Area And Perimeter Exercise 11.4 Tips:

**APPLICATIONS**

You must have observed that quite often, in gardens or parks, some space is left all around

in the form of path or in between as cross paths. A framed picture has some space left all

around it.

We need to find the areas of such pathways or borders when

we want to find the cost of making them.

**CIRCLES**

A racing track is semi-circular at both ends (Fig 11.27).

Can you find the distance covered by an athlete if he takes two rounds

of a racing track? We need to find a method to find the distances around

when a shape is circular.

**Circumference of a Circle**

Tanya cut different cards, in curved shape from a cardboard. She wants to put lace around Base Height Area of Triangle

15 cm **_ 87 cm** 31.4 mm 1256 mm 22 cm

**__**170.5 cm to decorate these cards. What length of the lace does she require for each? You cannot measure the curves with the help of a ruler, as these figures are not “straight”.

What can you do?

Here is a way to find the length of lace required for shape in Fig 11.28(a). Mark a

point on the edge of the card and place the card on the table. Mark the position of the

point on the table also

Now roll the circular card on the table along a straight line till

the marked point again touches the table. Measure the distance

along the line. This is the length of the lace required

. It is also the distance along the edge of the card

from the marked point back to the marked point.

You can also find the distance by putting a string on the edge

of the circular object and taking all round it.

The distance around a circular region is known as its circumference.

**Do This** Take a bottle cap, a bangle or any other circular object and find the circumference.

Now, can you find the distance covered by the athlete on the track by this method?

Still, it will be very difficult to find the distance around the track or any other circular

object by measuring through string. Moreover, the measurement will not be accurate.

So, we need some formula for this, as we have for rectilinear figures or shapes.

Let us see if there is any relationship between the diameter and the circumference of

the circles.

**Do This** Take one each of quarter plate and half plate. Roll once each of these on

a table-top. Which plate covers more distance in one complete revolution?

Which plate will take less number of revolutions to cover the length of the

table-top?

**Area of Circle**

Consider the following:

A farmer dug a flower bed of radius 7 m at the centre of a field. He needs to

purchase fertiliser. If 1 kg of fertiliser is required for 1 square metre area,

how much fertiliser should he purchase?

What will be the cost of polishing a circular table-top of radius 2 m at the rate

of 10 per square metre?

Can you tell what we need to find in such cases, Area or Perimeter? In such

cases we need to find the area of the circular region. Let us find the area of a circle, using

graph paper.

Draw a circle of radius 4 cm on a graph paper Find the area by counting

the number of squares enclosed.

As the edges are not straight, we get a rough estimate of the area of circle by this method.

There is another way of finding the area of a circle.

Draw a circle and shade one half of the circle Now fold the circle into

eighths and cut along the folds Arrange the separate pieces as shown,which is roughly a parallelogram.

The more sectors we have, the nearer we reach an appropriate parallelogram. As done above if we divide the circle in 64 sectors, and arrange these sectors. It

gives nearly a rectangle What is the breadth of this rectangle? The breadth of this rectangle is the radius of the

circle, i.e., ‘r’.

As the whole circle is divided into 64 sectors and on each side we have 32 sectors, the

length of the rectangle is the length of the 32 sectors, which is half of the circumference.

(Fig 11.37)

Area of the circle = Area of rectangle thus formed = l × b

= (Half of circumference) × radius = 1/2 X 2πrXr = πr2 So, the area of the circle = πr2

**Try These** Draw circles of different radii on a graph paper. Find the area by counting the

number of squares. Also find the area by using the formula. Compare the two answers.