NCERT solutions for Math - Magic [English] Class 5 chapter 11 - Area and its Boundary [Latest edition]

Parth and Gini bought aam papad (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

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?

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

Measure the yellow rectangle. It is ________ cm long.

How many stamps can be placed along its length?

How wide is the rectangle? ________ cm

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? ________ square cm

What is the perimeter of the rectangle? ________ cm

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

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

A thin wire 20 centimeters long is formed into a rectangle. If the width of this rectangle is 4 centimeters, what is its length?

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

How many tiles like the triangle given here will fit in the white design?

Area of design = ________ square cm

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

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?

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?

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?

Can you think of how to cut a postcard so that you can pass through it?

You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!

• How many of you can sit in one square meter?

You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!

• How many of you can stand in it?

You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!

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

You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!

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

Measure the length of the floor of your classroom in meters. Also, measure the width.

• What is the area of the floor of your classroom in square metres?

Measure the length of the floor of your classroom in meters. Also, measure the width.

• How many children are there in your class?

Measure the length of the floor of your classroom in meters. Also, measure the width.

• So how many children can sit in one square meter?

Measure the length of the floor of your classroom in meters. Also measure the width.

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

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 meter 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?

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

• 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 —

1. The perimeter of square A is __________ cm.

2. The side of square B is __________ cm.

3. The area of square B is __________ square cm.

4. The area of square B is __________ times the area of square A.

5. The perimeter of square B is __________ cm.

6. The perimeter of square B is __________ times the perimeter of square A.

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 motorboats 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)

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 motorboats in only one lake. The other lake will be saved for the birds to make their nests.

• What is the length of the boundary of lake B in the drawing?

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 motorboats in only one lake. The other lake will be saved for the birds to make their nests.

• How many kilometers long is the actual boundary of lake A?

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 motorboats in only one lake. The other lake will be saved for the birds to make their nests.

• How many kilometers long is the actual boundary of lake B?

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 motorboats in only one lake. The other lake will be saved for the birds to make their nests.

• 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?

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 motorboats in only one lake. The other lake will be saved for the birds to make their nests.

• Find the area of lake B on the drawing in square cm. What is its actual area in square km?

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 meters of wire and tried to make different rectangles.

He made a 10 m × 40 m rectangle. Its area was 400 square meters. So he next made a 30 m × 20 m rectangle.

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

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 meters of wire and tried to make different rectangles.

He made a 10 m × 40 m rectangle. Its area was 400 square meters. So he next made a 30 m × 20 m rectangle.

• What other rectangles can he make with 100 meters 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 meters.

• Why did Cheggu not choose a rectangle? Explain.

So Anar also tried many different ways to make a boundary for 800 square meters 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 get for these rectangles?

• A 
  Gold wire for A = _________ metres
• B 
  Gold wire for B = _________ metres
• C  
  Gold wire for C = __________ metres

But then Anar made an even longer rectangle... See how long!

• D 
  So he will get __________ metres of gold wire!!

Can you make a rectangle with a still longer boundary? I made a rectangle 1 cm wide and 80000 m long. Imagine how long that boundary will be!!! With that much gold wire I can become a king!