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Practice each question, then open the answer or worked solution.
Suggest some ways to find out whose piece is bigger. Discuss.
The length of piece A is 6 cm.
So 6 squares of side 1 cm can be arranged along its length.
The width of piece A is 5 cm.
So 5 squares can be arranged along its width.
Altogether 30 squares can be arranged on it.
So, the area of piece A = 6 cm × 5 cm = 30 square cm
Altogether how many squares can be arranged on it? ________
30
So the area of piece A = ________ square cm
So the area of piece A = 30 square cm
4. In the same way find the area of piece B.
Now, the area of piece B = 11 cm × 3 cm = 33 square cm
Who had the bigger piece? How much bigger?
So, the area of piece B is bigger than the area of piece A.
Difference in area of piece A and piece B = 33 − 30 = 3 square cm
So, piece B is 3 square cm bigger than piece A.
Cover with stamps:
This stamp has an area of 4 square cm. Guess how many such stamps will cover this big rectangle.
Check your guess:
a) Measure the yellow rectangle. It is ________ cm long.
14cm
b) How many stamps can be placed along its length? ________
7 stamps
c) How wide is the rectangle? ________ cm
8cm
d) How many stamps can be placed along its width? ________
4 stamps
e) How many stamps are needed to cover the rectangle? ________
28 stamps
f) How close was your earlier guess? Discuss.
It was pretty close.
g) What is the area of the rectangle? ________ Square cm
Area of rectangle = 7 × 4 = 28 square cm
h) What is the perimeter of the rectangle? ________ cm
Length of the rectangle = 14 cm
Breadth of the rectangle = 8 cm
A rectangle has 2 lengths and 2 breadths.
So, perimeter of the rectangle = Sum of all its sides = Length of its boundary = 14 cm + 8 cm + 14 cm + 8 cm = 44 cm
The perimeter of rectangle is 44 cm.
Practice time:
a) 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?
Given length of kitchen = 220 cm
Width of the kitchen = 180 cm
Each side of tile = 10 cm
Area of floor = length × width
= 220 × 180 = 39600 square cm
Area of a tile = side × side
= 10 × 10 = 100 square cm
Number of tiles = area of floor/ area of a tile
= 39600/100
= 396 tile.
b) The fencing of a square garden is 20 m in length. How long is one side of the garden?
Given perimeter of garden = 20 m which has to be fenced.
Length of one side = perimeter/4
= 20/5
= 5m.
c) A thin wire 20 centimeters long is formed into a rectangle. If the width of this rectangle is 4 centimeters, what is its length?
Given perimeter of a rectangle = 20 cm
Width of a rectangle = 4 cm
We know that perimeter of rectangle = 2 (length + breadth)
20 = 2 length + 2 breadth
2 length = 20 – 2 breadth
2 length = 20 – 2 × 4
2 length = 20 – 8
Length = 12/2
= 6 cm
d) A square carrom board has a perimeter of 320 cm. How much is its area?
Given perimeter of carrom board is 320 cm
We know that perimeter of square = 4 × side
Side = perimeter/4
Side = 320/4
= 80 cm
We know that area of square = side × side
= 80 × 80
= 6400 square cm
e) How many tiles like the triangle given here will fit in the white design? Area of design = ________ square cm
6 triangular tiles will fit in to the given white design.
Now, area of 1 such triangular tile = 12 square cm
Area of 6 triangular tiles that make this design = 6 × 12 = 3 square cm
Area of design = 3 square cm
f) Sanya, Aarushi, Manav and Kabir made greeting cards. Complete the table for their cards:
Perimeter of Sanya’s card = Sum of all its sides = 10 + 8 + 10 + 8 = 36 cm
Length of Manav’s card = 11 cm
Perimeter of his card = 44 cm
We have to find the width of Manav’s card.
Perimeter of card = Sum of all its sides = 11 + 11 + sum of 2 other sides = 22 + sum of 2 other sides
Now, sum of two other sides = 44 − 22 = 22 cm
The two other sides of the greeting cards are width.
So, width of Manav’s card = 22 ÷ 2 = 11 cm
Width of Aarushi’s card = 8 cm
Area of the card = 80 square cm
Now, we have to find length of the card.
Area of card = Length of card × 8 cm = 80 square cm
So, on dividing the area of card by its width, we can get its length.
Therefore, length of Aarushi’s card = 80 ÷ 8 = 10 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.
1. What is its area? What is its perimeter?
Length of paper sheet = 14 cm
Breadth of paper sheet = 9 cm
Area of the sheet = 14 cm × 9 cm = 126 square cm
Perimeter of the sheet = 14 cm + 9 cm + 14 cm + 9 cm = 46 cm
2. 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? _____
84 cm
3. What is its perimeter _____?
90 cm
Whose belt is the longest in the class? _____
Strips of the least width will make the longest belt in the class.