How Many Squares Chapter 3 Class 5 JKBOSE Solutions

“How Many Squares” is Chapter 3 from Merry Math V for students of Class 5th of JKBOSE. This post is about How Many Squares Chapter 3 Class 5 JKBOSE Solutions. In a previous post, you read about Shapes and Angles Chapter 2 Class 5 Math JKBOSE Solutions. Let’s get started:

How Many Squares Chapter 3 Class 5 JKBOSE Solutions

Page No. 35 Solutions

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

Ans. On measuring the side of the red square is 1 cm.

How many rectangles could you make? ________

Ans. We can make 7 rectangles.

(The length of the boundary is called the 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 longest perimeter?

Ans. Rectangles of size 1 x 12 have the longest perimeter.

Which of these rectangles has the smallest perimeter?

Ans. Rectangles of size 3 × 4 have the smallest perimeter.

Page No. 36 Solutions

Measure Stamps

Look at these interesting stamps.

(Stamp D covers 12 squares. Each square is of side 1 cm. So the area of Stamp D is 12 square cm)

(a) How many squares of one-centimetre side does stamp A cover? And Stamp B?

Ans. Stamp ‘A’ covers 18 squares of 1 cm. Stamp B covers 8 squares of 1 cm.

(b) 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? _______ squares cm. 

Ans. Stamp ‘A’ has the biggest area. This stamp covers 18 squares of side 1 cm. Its area is 18 square cm.

(c) Which two stamps have the same area?

How much is the area of each of these stamps? _______ square cm.

Ans. Stamps ‘D’ and ‘F’ have the same area.

The area of each of them is 12 square cm.

(d) The area of the smallest stamp is __________ square cm.

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

Ans. The area of the smallest stamp is 4 square cm.

The difference between the area of the smallest and the biggest stamp is 14 square cm. (18 – 4 = 14)

Page No. 37 Solutions

Guess

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

Ans. The page of this book has a bigger area than my footprints.

(b) Which has the smaller area — two five rupee notes together or a hundred – rupee note?

Ans. A hundred rupee note has a smaller area.

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

Ans. 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?

Ans. No, because 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?

No, because the perimeter of the yellow shape is less than the perimeter of the blue shape.

How Big is My Hand?

Trace your hand on the squared sheet on the next 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.

Ans. On a squared sheet of paper, trace your hand and your friend’s hand. Count the number of complete squares, half-filled squares, more than half-filled squares and less than half-filled squares.

Neglect the less than half-filled squares.

Take the sum of complete squares and more than half-filled squares to get the value of the area.

For Figure A: Number of complete squares = 6

Number of half-filled squares = 7

Number of more than half-filled squares = 6

Area of half-filled and more than half filled squares = 6 + 7/2 +6 = 6 + 3.5 + 6 = 15.5 square cm

For Figure B: Number of complete squares = 13

Number of half-filled squares = 4

Number of more than half-filled squares = 13

Area of half-filled and more than half filled squares = 13 + 6/2 + 13 = 13 + 3 + 13 = 29 square cm

Page No. 38 Solutions

My footprints

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

Ans. My footprint is larger than my friend’s footprint.

How will decide? 

Ans. We can decide by finding the area of these footprints.

Discuss

Is the area of both your footprints the same?

Ans. No, the area of both my footprints is not the same.

Page No. 39 Solutions

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

Ans. Chimpanji’s footprint may have the same area as mine footprint.

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

Ans. From the footprint of the hen, I think its area is 3 square cm (approx.)

From the footprint of the dog, I think its area is about 9 square cm.

Page No. 40 Solutions

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

Ans.

Let us name these prints as ‘a’, ‘b’, ‘c’, ‘d and ‘e’. Now make possible rectangles containing complete squares.

Area of print ‘a’ = 5 complete squares + 2 half squares + 7 more than half.

The approximate area of ‘a’ = (5 + 2 × ½ + 7) = 5 + 1 + 7 = 13 square cm.

Area of print ‘b’ = 7 complete squares + 2 half squares + 5 more than half.

The approximate area of ‘b’ = (7 + 2 × ½ + 5) = 7+ 1 + 5 = 13 square cm

Area of print ‘c’ = 6 complete square + 7 more than half

The approximate area of ‘c’ = 6 + 7 = 13 square cm.

Area of print ‘d’ = 5 complete square + 5 more than half

The approximate area of ‘d’ = 5 + 5 = 10 square cm.

Area of print ‘e’ = 98 complete squares + 4 half squares + 18 more than half.

The approximate area of ‘d’ = (98 + 4 × ½ +18) square cm = 98 +2 + 18 = 118 square cm

Area of the complete footprint = (13+ 13 + 13 + 10 + 118) = 167 square cm.

Page No. 41 Solutions

How many squares in Me?

What is the area of this triangle?

Ans. 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?

Ans. Hmmm, so its area is 4 square cm.

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

Ans. Area of triangle A = ½ of area of rectangle = ½  of area 12 square cm.

= 6 square cm.

Area of square B = 4 complete squares + 8 half squares + 4 quarter squares

= 4 + ½ × 8 + ¼ × 4 = 4 + 4 + l = 9 square cm

Area of C = 2 complete squares + 2 more than half.

= 2 + 2 = 4 square cm

Area of D = 5 complete squares + 2 half squares

= (5 + 2 × ½) = 5 + 1= 6 square cm

Area of shape E = 18 complete squares + 6 half squares

= 18 + 6 × ½ = 18 + 3 = 21 square cm.

Area of F = 4 complete squares + 4 more than half

= 4 + 4 = 8 square cm.

Page No. 42 Solutions

Try Triangles

Sakeena: Both the big triangles in this rectangle have the same area.

Suhail: But these look very different. 

Suhail: The blue triangle is half of the big rectangle.

The area of the big rectangle is 20 square cm.

So, the rectangle So the area of the blue triangle is 10 squares

Sakeena: And what about the red triangle?

Suhail: Ah, in it there are two halves of two different rectangles!

Explain.

Now you find the area of the two rectangles Suhail is talking about, what is the area of the red triangle?

Ans. Area of Rectangle A + Area of Rectangle B

= (3 × 4) square cm + (2 × 4) square cm = 12+ 8 =

20 square cm

So, the area of the red triangle is half of these two rectangles. Squares = 10 square cm.

Hence, both triangles have equal areas.

Suhail: Yes, you are right. And you know what!! You can draw many more triangles of an area of 10 square cm in this rectangle.

Try drawing them.

(Do yourself)

Page No. 43 Solutions

Complete the Shape

Tabassum 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.

Is he correct? Discuss. 

Ans. Yes, he is correct.

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

Sol. Green area = 2 complete squares + 4 half squares.

= 2 + (½ × 4) = 2 + 2 = 4 square cm

Yellow area = 3 complete square + 2 more than half + 2 half filled

= 3 + 2 + (½ × 2) = 3 + 2 + 1 = 6 square cm

Page No. 44 Solutions

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

Sol. Yes, Tabassum is correct.

Blue area = 2 complete squares + 4 more than half filled squares

= 2 + 4 = 6 square cm. 

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

Sol. Yes, I can do it some other ways as under:

Page No. 44 – 45 Solutions

Practice Time

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

Ans.

The completed shape = 2 complete square + 4 half squares

= 2 + (½ × 4) = 2 + 2 = 4 square cm

2. 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.

Ans.

If we draw two sides to complete the shape we get a rectangle. The area of this rectangle is 2 square cm. Now, draw a point just above the bottom vertex of the rectangle and join the given sides with this point. This will give a rectangle with an area of less than 2 square cm.

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

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

Ans.

One straight line is drawn in the given rectangle to divide it into two equal triangles as above.

Now, the Area of each triangle is half of the given rectangle.

Area of given rectangle = 20 square cm. 

So, the area of each of the triangles = 20/2 = 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?

Ans.

One straight line is drawn in the given rectangle to divide it into two equal rectangles as above.

Now, the Area of each rectangle is half of the given rectangle.

Area of given rectangle = 20 square cm.

So, the area of each of the smaller rectangles = 20/2 = 10 square cm.

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

Two straight lines are drawn in the given rectangle to divide it into one rectangle and two equal triangles as shown above.

Page No. 46 Solutions

What is the area of the rectangle?

Ans. You know, the area of the given rectangle = 20 square cm.

The area of the divided rectangle is half of the given rectangle.

So, the area of the new rectangle = 10 square cm.

What is the area of each of the triangles?

Ans. The area of the new rectangle is = 10 square cm.

Area of the each of the triangles is half of the new rectangle whose area is 10 square cm.

So, the area of each of the triangles = 5 square cm.

Puzzles with five squares
Measure the side of a small square on the squared paper. Make as many shapes as possible using 5 such squares.

Three are drawn for you.

Ans.

(a) How many different shapes can you draw?

Ans. I can draw 12 different shapes.

(b) Which shape has the longest perimeter? How much? ……….. cm.

Ans. All shapes (except number 11) have the longest perimeter. It is 12 cm.

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

Ans. Shape No. 11 has the shortest perimeter. It is 10 cm.

Page No. 47 Solutions

(d) What is the area of the shapes? ………..square cm.

Ans. The area of each of the shapes is 5 square cm.

Did you get all 12 shapes using 5 squares?

Ans. Yes, I got all the 12 shapes.

Page No. 50 Solutions

Make a pattern using your tile. Trace the shape to repeat it on a page, but remember there must be no gaps between them. Sumaira made a pattern using her yellow tiles.

Answers these-

How many tiles has she used?

Ans. She has used 12 tiles.

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

Ans. Area = length × breadth

= 12 x 3 = 36 square cm

Practice Time

Sumaira tried to make some other tiles. She started with a square of 2 cm side and made shapes like these.

Look at these carefully and find out:

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 tilling those shapes.

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

Ans. Shapes C and D will tile the floor without any gaps.
The area of these shapes = 2×2 = 4 square cm. The following designs can be made by using these shapes.
Design by using shape C:

Design by using shape D:

Some of the designs which can be made from a square are given below.

This can also be done using a triangular tile as follows:

That’s it about How Many Squares Chapter 3 Class 5 JKBOSE Solutions. Hope you have found it useful. Do share your views about this post in the comment section below.