NCERT solutions for Math - Magic [English] Class 5 chapter 3 - How Many Squares? [Latest edition]

Measure the side of the red square on the dotted sheet. Draw here as many rectangles as possible using 12 such squares.

How many rectangles could you make?

Each rectangle is made out of 12 equal squares, so all have the same area, but the length of the boundary will be different.

Which of these rectangles has the longest perimeter?

Each rectangle is made out of 12 equal squares, so all have the same area, but the length of the boundary will be different.

Which of these rectangles has the smallest perimeter?

Look at these interesting stamps.

How many squares of one-centimeter side does stamp A cover?

And stamp B?

Look at these interesting stamps.

Which stamp has the biggest area? How many squares of side 1 cm does this stamp cover? How much is the area of the biggest stamp? square cm.

Look at these interesting stamps.

Which two stamps have the same area? How much is the area of each of these stamps? square cm.

Look at these interesting stamps.

The area of the smallest stamp is ______ square cm.

The difference between the area of the smallest and the biggest stamp is ______ square cm.

Which has the bigger area - one of your footprints or the page of this book?

Which has the smaller area - two five-rupee notes together or a hundred rupee notes?

Look at a 10 rupee note. Is its area more than hundred square cm?

Is the area of the blue shape more than the area of the yellow shape? Why?

Is the perimeter of the yellow shape more than the perimeter of the blue shape? Why?

Trace your hand on the squared sheet on the page.
How will you decide whose hand is bigger-your hand or your friend’s hand?

What is the area of your hand? square cm.

What is the area of your friend’s hand? square cm.

Whose footprint is larger - yours or your friend’s?

How will you decide? Discuss.

Is the area of both your footprints the same?

Guess which animal’s footprint will have the same area as yours. Discuss.

Here are some footprints of animals in actual sizes. Guess the area of their footprints.

Hen

Dog

Make big squares and rectangles like this to find the area faster.

What is the area of this triangle?

The triangle is half the rectangle of an area of 2 square cm. So its area is ______ square cm.

Is this shape half of the big rectangle?

Hmmm...... So its area is ______ square cm.

Write the area (in square cm) of the shapes below:

Suruchi drew two sides of a shape. She asked Asif to complete the shape with two more sides so that its area is 10 square cm.

He completed the shape like this.

How did you do this?

Oh, that's easy! If you look at the green area it is 4 square cm. Below it is the yellow area of 6 square cm. So the area of my shape is 10 square cm!

Is he correct? Discuss.

Explain how the green area is 4 square cm and the yellow area is 6 square cm.

Oh, I thought of doing it differently! If you draw like this, the area is still 10 square cm.

Is Suruchi correct? How much is the blue area? Explain

Can you think of some other ways of completing the shape?

Try some other ways yourself.

Now ask your friends to solve these at home.

This is one of the sides of a shape. Complete the shape so that its area is 4 square cm

Two sides of a shape are drawn here. Complete the shape by drawing two more sides so that its area is less than 2 square cm.

Here is a rectangle of an area of 20 square cm.

Draw one straight line in this rectangle to divide it into two equal triangles. What is the area of each of the triangles?

Here is a rectangle of an area of 20 square cm.

Draw one straight line in this rectangle to divide it into two equal rectangles. What is the area of each of the smaller rectangles?

Here is a rectangle of an area of 20 square cm.

Draw two straight lines in this rectangle to divide it into one rectangle and two equal triangles.
What is the area of the rectangle?
What is the area of each of the triangles?

Measure the side of a small square on the squared paper given below. Make as many shapes as possible using 5 such squares. Three are drawn for you.

How many different shapes can you draw?

Measure the side of a small square on the squared paper given below. Make as many shapes as possible using 5 such squares. Three are drawn for you.

Which shape has the longest perimeter? How much? _______ cm

Measure the side of a small square on the squared paper given below. Make as many shapes as possible using 5 such squares. Three are drawn for you.

Which shape has the shortest perimeter? How much? _______ cm

Measure the side of a small square on the squared paper given below. Make as many shapes as possible using 5 such squares. Three are drawn for you.

What is the area of the shapes? _______ square cm. That’s simple!

Did you get all the 12 shapes using 5 squares?

Draw all the 12 shapes on a sheet of cardboard and cut them.

Try to arrange your 12 shapes in some other way to make a 10 × 6 rectangle. Could you do it?

You have to make a 5 × 12 rectangle with these 12 shapes. There are more than 1000 ways to do it. If you can find even one, that’s great!

Can you find the tile which is repeated to make each of these floor patterns? Circle a tile in each pattern.

How many tiles has she used?

What is the area of the floor pattern Ziri has made here?

Which of these shapes will tile a floor (without any gaps)? Discuss. What is the area of these shapes?

Make designs in your copy by tiling those shapes.

Now you create your own new tiles out of a square. Can you do the same with a triangle? Try doing it.