Welcome, Guest  0 
ekShiksha : Privacy Setting
11. Area and its Boundary
Whose Slice is Bigger?
Parth and Gini bought aam paapad (dried mango slice) from a shop. Their pieces looked like these.
Both could not make out whose piece was bigger.
 Suggest some ways to find out whose piece is bigger. Discuss.
A friend of Parth and Gini showed one way, using small squares.
The length of piece A is 6 cm.
So 6 squares of side 1 cm can be arranged along its length.
The width of piece A is 5 cm.
So 5 squares can be arranged along its width.
 Altogether how many squares can be arranged on it?
 So the area of piece A = square cm
 In the same way find the area of piece B.
 Who had the bigger piece? How much bigger?
Cover with Stamps
This stamp has an area of 4 square cm. Guess how many such stamps will cover this big rectangle.
Check your guess
 Measure the yellow rectangle. It is _____ cm long.
 How many stamps can be placed along its length?
 How wide is the rectangle?
 How many stamps can be placed along its width?
 How many stamps are needed to cover the rectangle?
 How close was your earlier guess? Discuss
 What is the area of the rectangle?
 What is the perimeter of the rectangle?
My Belt is Longest!
Take a thick paper sheet of length 14 cm and width 9 cm. You can also use an old postcard.
 What is its area? sq.cm What is its perimeter? cm.
 Now cut strips of equal sizes out of it.
Using tape join the strips, end to end, to make a belt.
 How long is your belt?
 What is its perimeter
 Whose belt is the longest in the class?
Discuss
 Why did some of your friends get longer belts than others?
 Is the area of your belt the same as the area of the postcard? Why or why not?
 What will you do to get a longer belt next time?
Puzzle: Pass through a Postcard
Can you think of how to cut a postcard so that you can pass through it? (See photo.) If you have tried hard enough and still not got it… look for the answer somewhere ahead.
People People Everywhere

You can play this game in a ground.
Make two squares of one square metre each.
Divide your class in two teams. Ready to play!
With four MathMagic books in a line you can get the length of around one metre 9 cm. Try these in your teams  How many of you can sit in one square metre?
 How many of you can stand in it?
 Which team could make more children stand in their square? How many?
 Which team could make more children sit in their square? How many?
 Measure the length of the floor of your classroom in metres. Also measure the width
 What is the area of the floor of your classroom in square metres?
 How many children are there in your class?
 So how many children can sit in one square metre?
 If you want to move around easily then how many children do you think should be there in one square metre?
Share the Land
Nasreena is a farmer who wants to divide her land equally among her three children  Chumki, Jhumri and Imran. She wants to divide the land so that each piece of land has one tree. Her land looks like this.
 Can you divide the land equally? Show how you will divide it. Remember each person has to get a tree. Colour each person’s piece of land differently.
 If each square on this page is equal to 1 square metre of land, how much land will each of her children get? square m Chumki, Jhumri and Imran need wire to make a fence.
 Who will need the longest wire for fencing?
 How much wire in all will the three need?
 Look at the table. If you were to write the area of each of these which column would you choose? Make a (√ ).
 Draw a square of 9 square cm. Write A on it.
Draw another square with double the side. Write B on it.
Answer these 
 The perimeter of square A is cm.
 The side of square B is cm.
 The area of square B is square cm.
 The area of square B is times the area of square A.
 The perimeter of square B is cm.
 The perimeter of square B is times the perimeter of square A.
Thread Play
Take a 15 cm long thread. Make different shapes by joining its ends on this sheet.
 Which shape has the biggest area? How much? What is the perimeter of this shape?
 Which shape has the smallest area? How much? What is the perimeter of this shape?
Also make a triangle, a square, a rectangle and a circle. Find which shape has biggest area and which has the smallest.
Save the Birds
There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motor boats in only one lake. The other lake will be saved for the birds to make their nests.
 How many cm is the length of the boundary of lake A in the drawing? (use thread to find out)
 What is the length of the boundary of lake B in the drawing?
 How many kilometres long is the actual boundary of lake A ?
 How many kilometres long is the actual boundary of lake B?
 A longer boundary around the lake will help more birds to lay their eggs. So which lake should be kept for birds? Which lake should be used for boats?
 Find the area of lake B on the drawing in square cm. What is its actual area in square km?
King's Story
The King was very happy with carpenters Cheggu and Anar. They had made a very big and beautiful bed for him. So as gifts the king wanted to give some land to Cheggu, and some gold to Anar.
Cheggu was happy. He took 100 metres of wire and tried to make different rectangles.
He made a 10 m * 40 m rectangle. Its area was 400 square metres.
So he next made a 30 m * 20 m rectangle.
 What is its area? Is it more than the first rectangle?
 What other rectangles can he make with 100 metres of wire? Discuss which of these rectangles will have the biggest area. Cheggu’s wife asked him to make a circle with the wire. She knew it had an area of 800 square metres.
 Why did Cheggu not choose a rectangle? Explain
 He made rectangles A, B and C of different sizes. Find out the length of the boundary of each. How much gold wire will he get for these rectangles?