# Area And Its Boundary

Page 146

Whose Slice is Bigger?

Suggest some ways to find out whose piece is bigger. Discuss.

Method 1

Cut piece B into 3 pieces as shown in fig.

Now put parts 1 and 2 over piece A as shown in fig.

Parts 1 and 2 exactly cover piece A but part 3 of piece B is left remaining. Therefore, we can conclude that piece B is bigger.

Method 2

Divide piece A and B into square boxes of 1 sq cm and count the total boxes that cover piece A and B.

Piece A = 30 boxes

Piece B = 33 boxes

Therefore, piece B is bigger.

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Altogether how many squares can be arranged on it?

So the area of piece A = __30__ square cm.

In the same way, find the area of piece B.

Area of piece B = 33 sq cm.

Who had the bigger piece? How much bigger?

Piece B is bigger.

33 – 30 = 3 sq cm

Piece B is bigger in area by 3 sq cm.

Cover with Stamps

This stamp has an area of 4 square cm. guess how many such stamp will cover this rectangle.

Ans: my guess is 25 stamps.

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Check your guess

a). measure the yellow rectangle. It is __14__ cm long.

b). How many stamps can be placed along its length?

Ans: 7 stamps

c). How wide is the rectangle?

Ans: 8 cm.

d). How many stamps can be placed along its width?

Ans: 4 stamps

e). How many stamps are needed to cover the rectangle?

Ans: 28 stamps

f). How close was your earlier guess? Discuss.

Ans: It was pretty close.

g). What is the area of the rectangle?

Ans: Area of the rectangle is 4 X 28 = 112 sq cm

h). What is the perimeter of the rectangle?

Ans: Perimeter of the rectangle = 14 + 8 + 14 + 8 = 44 cm.

Practice Time

a). Arbaz plans to tile his kitchen floor with green square tiles. Each slide of the tile is 10 cm. His kitchen is 220 cm in length and 180 cm wide. How many tiles will you he need?

Area of the floor = length X breadth

= 220 X 180

= 39600 sq cm

Area of the tile = side X side

= 10 X 10

= 100 sq cm

Number of tiles = Area of the floor ÷ Area of the tile

= 39600 ÷ 100

= 396

b). The fencing of a square garden is 20m in length. How long is one side of the garden?

Length of the fencing = perimeter of the square garden

Perimeter = 4 X side

20 = 4 X side

Side = 20 ÷ 4

= 5 m

c). A thin wire 20 centimetres long is formed into a rectangle. If the width of this rectangle is 4 centimetres. What is its length?

Width of the rectangle = 4 cm

Perimeter = 20 cm

Perimeter = 2(length + width)

2 (length + width) = perimeter

2 (length + 4) = 20

Length + 4 = 20 ÷ 2

Length + 4 = 10

Length = 10 – 4

Length = 6 cm

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d). A square carom board has a perimeter of 320 cm. How much is its area?

Perimeter of square carrom board = 4 X side

Perimeter of square carrom board = 320 cm

4 X side = 320

Side = 320 ÷ 4

= 80 cm

Area = side X side

= 80 X 80

= 6400 sq cm

e). How many tiles like the triangle given here will fit int the white design?

Ans: 6 tiles

Area of design = __6 X ½__ = __3__ square cm.

* Make your own designs of areas 4 and 6 square cm.

f). Sanya, Aarushi, Manav and Kabir made greeting cards. Complete the table for their cards.

Whose card | Length | Width | Perimeter | Area |

Sanya | 10 cm | 8 cm | ||

Manav | 11 cm | 44 cm | ||

Aarushi | 80 square cm | |||

Kabir | 40 cm | 100 square cm |

Answer:

Sanya

Length = 10 cm

Width = 8 cm

Perimeter = 2(length + width)

= 2 (10 + 8)

= 2 (18)

= 36 cm

Area = length X width

= 10 X 8

= 80 sq cm

Manav

Length = 11cm

Perimeter = 44 cm

Width = ?

Perimeter = 2(length + width)

2(length + width) = Perimeter

2 (11 + width) = 44

11 + width = 44 ÷ 2

Width = 22 – 11

Width = 11 cm

Area = length X width

= 11 X 11

= 121 sq cm

Aarushi

Width = 8 cm

Area = 80 sq cm

Area = length X width

80 = length X 8

Length X 8 = 80

Length = 80 ÷ 8

= 10 cm

Perimeter = 2(length + width)

= 2 (10 + 8)

= 2 (18)

= 36 cm

Kabir

Perimeter = 40 cm

Area = 100 sq cm

Perimeter = 2(length + width)

2(length + width) = 40

Length + width = 40 ÷ 2

Length + width = 20

Area = length X Width

Length X width = 100

Factorize 100 such that both the factors add upto 100

2 X 50 = 100 but 2 + 50 = 52

4 X 25 = 100 but 4 + 25 = 29

5 X 20 = 100 but 5 + 20 = 25

10 X 10 = 100 and 10 + 10 = 20

Therefore, length = 10 cm

Width = 10 cm

Whose card | Length | Width | Perimeter | Area |

Sanya | 10 cm | 8 cm | 36 cm | 80 sq cm |

Manav | 11 cm | 11 cm | 44 cm | 121sq cm |

Aarushi | 10 cm | 8 cm | 36 cm | 80 square cm |

Kabir | 10 cm | 10 cm | 40 cm | 100 square cm |

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? What is its perimeter?

Length = 14 cm

Width = 9 cm

Area = length X width

= 14 X 9

= 126 sq cm

Perimeter = 2(length + width)

= 2(14 + 9)

= 2(23)

= 46 cm

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Now cut the strips of equal sizes out of it. Using tape join the strips, end to end, to make a belt.

Strips of width 1 cm.

We can make 9 strips of width 1 cm and length of each strip is 14 cm.

Joining 9 strips we get total length = 14 X 9 = 126 cm

Strips of width 3 cm.

We can make 3 strips of width of 3 cm and length of each strip is 14 cm.

Joining 3 strips we get total length = 14 X 3 = 42 cm

How long is your belt?

Ans: Suppose I made a belt of width 3 cm

Length of the belt is 42 cm.

What is its perimeter.

Perimeter = 2(length + width)

= 2(42 + 3)

= 2(45)

= 90 cm

Suppose I made a belt of width 1 cm

Length of the belt is 126 cm.

What is its perimeter.

Perimeter = 2(length + width)

= 2(126 + 1)

= 2(127)

= 254 cm

Whose belt is the longest in the class?

Ans: The strips that have least width are longest in the class.

Discuss

Why did some of your friends get longer belts than others?

Ans: Because they made the belts with least width.

Is the area of your belt the same as the area of the postcard?

Ans: Yes, area of the belt is the same as the area of the postcard.

Area of all the belts with different width have the same area it is because every part of the post card is used to make the belt.

What will you do to get a longer belt next time?

Ans: By making thinner belts we get a longer belt.

Page 151

People People Everywhere

A). You can play this game in the ground. Make two squares of one square metre each. Divide your class into two teams. Ready to play!

Try these in your teams-

How many of you can sit in one square metre?

Ans: Four.

How many of you can stand in it?

Ans: six.

Which team could make more children stand in their square? How many?

Ans: Team B can make six students stand in their square.

B). 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?

Length = 6 m

Width = 5 m

Area = length X width

= 6 X 5

= 30 sq m

How many children are there in your class?

Ans: 40

So how many children can sit in one square metre?

Children can sit in 1sq metre = ^{No.of children}/_{Area of class room}

= ^{40}/_{30}

= ^{4}/_{3}

= 1.33

Ans: Approximately 1 student can sit in 1 sq m

If you want to move around easily then how many children do you think should be there in one square metre?

Ans: Two.

Page 152

Can you imagine how big a square of side 1 km is? It has an area of __1__ square km.

Guess how many people can live on that.

Ans: About 1000 people can live on that.

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.

Page 153

If each square on this page is equal to 1 square metre of land, how much land will each of her children get?

Ans: 30 sq m.

Chumki, Jhumri and Imran need wire to make a fence.

Who will need the longest wire for fencing?

Ans: Jhumri will need the longest wire for fencing.

How much wire in all will the three need?

Chumki

Length of the fence = 5 + 6 + 5 + 6 = 22 m

Jhumri

Length of the fence = 3 + 10 + 1 + 3+ 5 + 2 + 3 + 5

= 32 m

Imran

Length of the fence = 3 + 2 + 5 + 3 +8 + 5

= 26 m

Total wire needed = 22 + 32 + 26

= 80 m

Practice Time

A). Look at the table. If you were to write the area of each of these which column would you choose? Make (√).

Answer:

Square cm | Square metre | Square km | |

Handkerchief | √ | ||

Sari | √ | ||

Page of you book | √ | ||

School land | √ | ||

Total land of a city | √ | ||

Door of your classroom | √ | ||

Chair Seat | √ | ||

Blackboard | √ | ||

Indian flag | √ | ||

Land over which a river flows | √ |

Page 154

B). Draw a square of 9 square cm. Write A on it. Draw another square with double the side. Write B on it.

Side of A = 3 cm

Side of B = 6 cm

Answer these –

1). The perimeter of square A is __12__ cm.

2). The side of square B is __6__ cm.

3). The area of square B is __36__ sq cm.

4). The area of square B is __4__ times the area of Square A.

5). The perimeter of square B is __24__ cm.

6). The perimeter of square B is __2__ times the perimeter of Square A.

Page 155

Thread Play

Take a 15 cm long thread. Make different shapes by joining its ends on this sheet.

A). Which shape has the biggest area? How much?

Do it yourself.

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.

a). How many cm is the length of the boundary of lake A in the drawing?

Ans: 33 cm

b). What is the length of the boundary of lake B in the drawing?

Ans: 26 cm

c). How many kilometres long is the actual boundary of lake A?

Ans: 33 km

d). How many kilometres long is the actual boundary of lake B?

Ans: 26 km

e). 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?

Ans: Lake A

f). find the area of lake B on the drawing in square cm. What is its actual area in square km?

King’s Story

Cheggu made a 30 X 20 m rectangle.

What is its area? Is it more than the first rectangle?

Ans: Area of rectangle = 30 X 20 = 600 sq m

It is 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?

Other possible rectangles are

5 X 45 = 225 sq m

15 X 35 = 525 sq m

25 X 25 = 625 sq m

The square with side 25 m 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 sq metres.

Why did Cheggu not choose a rectangle? Explain.

Ans: Because all the rectangles have area less than 800 sq m.

So Amar also tried to many different ways to make a boundary for 800 square metres of land.

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 getfor these rectangles?

A). 40 X 20 m

Perimeter = 2(length + width)

= 2(40 + 20)

= 2 (60)

= 120 metre

Gold wire for A = __120 __ metres.

B). 80 m X 10 m

Perimeter = 2(length + width)

= 2(80 + 10)

= 2 (90)

= 180 metre

Gold wire for B = __180 __ metres.

C). 800 X 1 m

Perimeter = 2(length + width)

= 2(800 + 1)

= 2 (801)

= 1602 metre

Gold wire for C = __1602 __ metres.

But then Amar made as even longer rectangle ……. See how long!

8000 m X 0.1

Perimeter = 2(length + width)

= 2(8000 + 0.1)

= 2 (8000.1)

= 16000.2 metre

So he will get __16000.2 __ metres of gold wire!!

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