13. Fields and Fences

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Rahmat is a farmer. He grows wheat in his field.

Farmer looking at his field.

I need a fence around my field.

How much wire hould I buy?

Rahmat needs to find the length of the boundary of the field. Can you find it from this picture? See the length of each side written near it.

Farmer measuring the length of his farm.

9 metre

9 metre

21 metre

15 metre


Uhm---m! The boundary is 54 metres long.

Farmer holding a roll of wire.
Rahmat bought a roll of 70 m wire for the fence.

Farmer holding a roll of wire.

A man named Ganpat.


I should also do the same for my field.

Ganpat asking for the leftover wire.

Can you give me the wire that is left with you? I will use  it for my field.


Oh sure, why not

Ganpat putting wire along his field. Breadth of the field is 18m and length is 9m straight and then 15 m in slant.

Ganpat thanked Rahmat and started fencing his own field. But he needed to get more wire.

How long is the boundary of Ganpat's field?

How much more wire will Ganpat need for his field?

Practice Time

  1. Here are pictures of some more fields. Find out which one has the longest boundary.


A trapezium shaped field with parallel sides of length 24 metre and 6 metre. Non parallel sides are 15 metre each.
Boundary = __________ metre


A field with breadth 12 m and length 9 m. Opposite side to this is 6 m and then turning left by 6 m and then moving up by 3 m and lastly turning left by 6m to complete the figure.
Boundary = __________ metre


A triangle shaped field with three sides as 9 metre, 12 metre and 15 metre.
Boundary = __________ metre


A six sided field with dimensions 15 metre, 9 metre and 15 metre. The same set of dimensions are repeated for opposite sides.
Boundary = __________ metre

An old man walking along a rectangular field with length 150 m and breadth 100 m.

  1. Chandu's father is called the 'young old man' in his village.

At 70 years of age, he is fully fit. Do you know his secret?

He goes for a walk around the field every morning. Everyday he takes four rounds of Chandu's field.

  • What is the total distance he covers?

4 × ______ = ______m= ______km

  1. Ganpat's wife works in a tailor's shop. She has to fix lace around a table cloth.

She bought a 100 metre roll of lace.

  • Look at the picture of the table cloth and tell how much lace is used for one table cloth.

A rectangular table cloth with length 59 cm and breadth 1m 50 cm.

  • How much lace will be used in 3 such table cloths?

  • How much lace will be left in the roll?


  1. Find out the length of the boundary of these shapes. (Hint:-You can use a thread)

Four different shapes A, B,C, and D are given in a box made with small squares.

Now count the squares to find out:

  • How many squares are there in each shape?
  • Which shape covers the least number of squares?
  • Which shape covers the most number of squares?

  1. Take a 20 centimetre long thread. Make different shapes by joining the ends. Place on the squared sheet on the next page.

Find out:

  • How many squares are there in each shape?
  • Which is the biggest shape?
  • Which is the smallest shape?
  • How long is the boundary of each shape?

Children could be asked to ignore a square if it is less than half, but count it as 1 if is more than half. This will give them a feel for' rounding off.

  1. How many different shapes can you make by joining two squares? Draw them on the squared sheet given below. How long is the boundary of each shape?

A big box made up of small squares. Two squares are joined and coloured.  Try this activity with three squares also.

Practice Time

  1. A square has a boundary of 12 cm.
  1. From the corner of this £ square, a small square of side 1 cm is cut off. Will the boundary of B be less or more? Find its length.
  2. If you cut a 1 cm square to m get shape C, what will be the £ length of the boundary of C?

Square 'A' has side as 3 cm. A 1 cm square is cut from the corner to get square 'B.' A 1 cm square is cut from middle of a side of square 'A' to get a new shape 'C.'
Square- New shape

  1. a) Find the length of the boundary of square D.
  1. b) 8 squares of side 1 cm are cut out of the square D. Now it looks like shape E. What is the length of the boundary of shape E?

Square 'D' with side equal to 5cm.  8 squares of side 1 cm are cut out of the square 'D' to get square 'E'.

  1. The boundary of this Square of side 1cm.  1cm _+_+_+_+_ is

Can we also say that the boundary is 4 x 1 cm?

  1. A hockey field is 91 metres 40 cm long and 55 metres wide. How long is the boundary of the field?
  2. Usha and Valsamma are running a race. Usha is running on the inner circle. Valsamma is running on the outer circle.

Two girls are running a race on a circular track.

Valsamma runs faster than Usha. But still she loses the race. Can you guess why?

Three girls are starting to race from different points.

Have you seen any race where runners start from different places — like in this picture?

Guess why?

School Garden

The students of Class III and IV thought of making a vegetable garden. They chose a place which looked like this.

A group of students is standing with Garden 1 and another group is standing with Garden 2. There is a path between both gardens.
Garden 1 - Garden 2

Students of both the classes thought that garden 1 was bigger. So both wanted to take garden 1. Suddenly Neetu said -

Two children talking about the size of gardens.
I think both gardens are equally big.

Quite possible! Let us find out if you are right.

  • How will Neetu find out if the two gardens are equally big?

A boy arranging books on a table.


  1. Look at the table in your classroom. Guess how many Math-Magic books you can place on it.

(Remember — The books should not overlap. Do not leave gaps between the books.)

Write your guess here.

Now check if your guess was right. How many books could you place?

What is the difference between your guess and the actual number

of books?

  1. Now look for another table.
  1. Is this table bigger than the last table? Yes/No
  2. MakeaguesshowmanyMath-Magicbookscanbekepton this table.

  3. Checkifyourguesswascorrect.

How many Math-Magic books could you keep?__

  1. The difference between the sizes of the two tables is __ books.
  1. a) How many Math-Magic books can be covered with one sheet of newspaper?
  1. Try covering your Math-Magic book with half a sheet of newspaper.
  2. Can you cover your book with a smaller sheet?

  1. Find the smallest sheet which can cover your book. Check if your friend used a smaller sheet than you did.

  1. a) Which is the biggest leaf in this picture?

Four leaves are drawn in a box made up of small squares.

  1. Collect some leaves from the garden. Place each of them here on this squared sheet. Trace out their edges and check how many squares there are in each leaf.
  2. Which is the biggest leaf?
  3. Which is the smallest leaf?

  1. a) How many small squares of size 1 cm are there in this big green square?
  1. Can you think of a faster way to know the total number of small squares without counting each?

A big square made up of small squares.

  1. Guess how many squares of one centimetre can fill this blue rectangle.

A rectangle with small squares on two of its sides.

Write your guess here.

Check your guess by filling it with small squares.

  1. Look at the picture. Can you divide it into 4 equal pieces? Each piece should have the same number of squares.

A staircase shaped figure with squares drawn inside.

Puzzle: A House and the Well

Raghavan has apiece of land.

There are 4 houses on his land and in the middle there is a well.

He wants to divide this land equally among his four children. Each should get one house and be able to use the well without

entering the other's land. Can you help him divide the land?

Give different colours to each one's share.

A land divided in 4 rows and 4 columns. There is a well in the middle of the land. Row 1 has a house in the last square. Row 2 has it in third square. Row 3 has it in second square and Row 4 has it in first square.