# How Many Squares?

Page 34

Measure the side of the square on dotted sheet. Draw as many rectangles as possible using 12 such squares. How many rectangles could you make?

We can make 7 right angles.

Which of these rectangles has the longest perimeter?

Rectangles 1 and 2 have the longest perimeter.

Which of these rectangles has the smallest perimeter?

Rectangles 4, 5, 6 and 7 have the smallest perimeter.

Page 35

Look at these interesting stamps.

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

And stamp B?

Stamp A covers 18 squares of one centimeter and Stamp B covers 8 square cm.

b). Which stamp has the biggest area?

Stamp A has the biggest area.

How many squares of side 1cm does this stamp cover?

It covers 18 squares of side 1 cm.

How much is the area of the biggest stamp?

The area of the biggest stamp is 18 square centimeters.

c). Which stamp has the same area?

Stamp B and stamp F have the same area.

d). How much is the area of each of these stamps?

The area of each of these stamps is 12 square cms.

The area of the smallest stamp is __4__ sq cms.

Page 36

a). Which has the bigger area one of your footprints or the page of this book?

The page of the textbook has a bigger area.

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

A hundred rupee note has a smaller area.

c). look at a 10 rupee note. Is its area more than a hundred square cm?

No. Its area is less than a hundred square cm.

d). is the area of the blue shape more than the area of the yellow shape? Why?

The area of the blue shape is equal to the area of the yellow shape.

e). Is the perimeter of the yellow shape more than the perimeter of the blue shape? Why?

The perimeter of the yellow shape is less than the perimeter of the blue shape.

How will you decide whose hand is bigger- your hand or your friend’s hand?

We will decide whose hand is bigger using graph paper. A graph paper contains square boxes of 1cm. Place the hands on graph paper and draw the outer curve of the hands. Then count the boxes in the outline. Count the boxes as complete boxes, half-filled boxes, boxes filled more than half. Don’t count the boxes filled less than half. From the total of complete, half-filled, and more than half-filled boxes we will decide the area of whose hand is bigger.

What is the area of your hand?

What is the area of your friend’s hand?

Page 37

Whose footprint is larger yours or your friend’s?

How will you decide? Discuss.

We can decide by finding the areas of the footprints using graph paper.

Is the area of both your footprints the same?

Page 38

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.

Area of the footprints of hen = between 2 to 3 square cm.

Area of the footprints of dog = between 5 to 7 square cm.

Page 39

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

Page 40

What is the area of this triangle?

The triangle is half the rectangle of an area of 2 square cm. So its area is __1__ square cm.

Is this shape half of the big rectangle?

Yes. This shape is half of the big rectangle.

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

Area of shape A:

Number of completely filled boxes = 4

Number of more than half-filled boxes = 0

Number of half-filled boxes = 2 boxes it means 1

Area of the shape A = 4 + 0 + 1 = 5 square cm

Area of shape B:

Number of completely filled boxes = 4

Number of more than half-filled boxes = 0

Number of half-filled boxes = 8 boxes it means 4

Area of the shape B = 4 + 0 + 4 = 8 square cm

Area of shape C:

Number of completely filled boxes = 2

Number of more than half filled boxes = 4

Number of half filled boxes = 0

Area of the shape C = 2 + 4 + 0 = 6 square cm

Area of shape D:

Number of completely filled boxes = 4

Number of more than half-filled boxes = 0

Number of half-filled boxes = 2 boxes it means 1

Area of the shape D = 4 + 0 + 1 = 5 square cm

Area of shape E:

Number of completely filled boxes = 18

Number of more than half-filled boxes = 0

Number of half-filled boxes = 6 boxes it means 3

Area of the shape E = 18 + 0 + 3 = 21 square cm

Area of shape F:

Number of completely filled boxes = 4

Number of more than half-filled boxes = 4

Number of half-filled boxes = 4 boxes it means 2

Area of the shape F = 4 + 4 + 2 = 10 square cm

Page 41

The blue triangle is half of the big rectangle. The area of the big rectangle is 20 square cm. So the area of the blue triangle is __________ square cm.

Area of the big rectangle = 20 square cm

Area of the blue triangle = half of 20 square cm

= 10 square cm

And what about the red triangle?

Area of the red triangle – 10 square cm

Ah, in it there are two halves of two different rectangles! Now you find the area of the two rectangles.

Area of the rectangle 1 = 12 square cm

half the area of rectangle 1 = 6 square cm

Area of the rectangle 2 = 8 square cm

half the area of rectangle 2 = 4 square cm

Area of the red triangle = 6 + 4 = 10 square cm

What is the area of the red triangle? Explain.

Area of the red triangle = 6 + 4 = 10 square cm

Page 42

Is he correct? Discuss.

Yes, he is correct.

Area of the green shape = 4 square cm

Area of the yellow shape = 6 square cm

Total area = 4 + 6 = 10

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

Area of green shape:

Number of completely filled boxes = 2

Number of more than half-filled boxes = 0

Number of half-filled boxes = 4 boxes it means 2

Area of the green shape F = 2 + 0 + 2 = 4 square cm

Area of red shape:

Number of completely filled boxes = 3

Number of more than half-filled boxes = 2

Number of half-filled boxes = 2 boxes it means 1

Area of the red shape F = 3 + 2 + 1 = 6 square cm

Page 43

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

Yes, Suruchi is also correct.

The area of the blue shape = 4 square cm.

Number of completely filled boxes = 2

Number of more than half filled boxes = 0

Number of half filled boxes = 4 boxes it means 2

Area of the red shape F = 2 + 0 + 2 = 4 square cm

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

Try some other ways yourself.

Page 44

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

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

Area of each of the triangles = 10 square cm.

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

Area of each of the smaller rectangles = 10 square cm

c). Draw two straight lines in this rectangle to divide it into one rectangle and two equal triangles.

What is the area of the rectangle?

Area of the rectangle = 10 square cm

What is the area of each of the triangles?

Area of each of the triangles = 5 square cm

Page 45

a). how many different shapes can you draw?

12

b). which shape has the longest perimeter? How much?

All the shapes have the same perimeter except shape.

Perimeter = 12 cm

c). Which shape has the shortest perimeter? How much?

Shape has the shortest perimeter.

The perimeter of the shortest shape is 10 cm

d). What is the area of these shapes?

The area of all the shapes is the same as they all are made of 5 square boxes.

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