Use the squares to find out:
1) What is the length and width of the library.
2) What is at the east side of the office?
3) What is the width of the garden?
4) Which class is located at the opposite side of std - 7.
5) Whose area is more, out of the assembly ground and play ground?
Answers
A square stamp has an area of 4 square cm. You need to find how many such stamps you can fit in the rectangle given below:
area of a rectangle
The rectangle is 10 cm long and 20 cm wide. How would you do solve this? One way is to place the stamps on the rectangle and count them. Simple, but a long process. Let’s look at another way:
How many stamps can you place along the length of the rectangle? The stamp is a square having an area of 4 square cm. This means that the length of its side is 2cm. Now, since the rectangle is 10 cm long and the stamp is 2 cm long, you can place 5 stamps along the length of the rectangle.
Also, you can place 10 stamps along the width of the rectangle. Hence, the total number of stamps that you can place is 5 x 10 = 50 stamps. You can try placing the stamps on the rectangle and count them to cross check.
Check out our detailed article on Area of a Square here.
Exercise 2
You have a square carrom board whose perimeter is 320 cm. Calculate its area.
area of a rectangle
Since the carom board is a square, all its sides are equal. Also, we know that the perimeter of the board is 320 cm. Hence, the length of each side of the carom board is 320/4 = 80 cm … we divided the perimeter by 4 since the square has 4 sides. Now, the area of the board is 80 x 80 = 6400 square cm.
The Belt Puzzle to understand Perimeter and Area of a Rectangle
Take a thick sheet of paper having a length of 14 cm and width of 9 cm. Answer the following questions:
What is its area?
What is its perimeter?
By now, you understand that to calculate the perimeter and area of a rectangle, you don’t have to use the small squares method. Instead, you can calculate it as follows:
Perimeter of the rectangular sheet = length + length + breadth + breadth
= 2 (length + breadth)
= 2 (14+9) = 2 x 23 = 46 cm.
Area of the rectangular sheet = length x breadth
= 14 x 9 = 126 square cm.
Now, take three such rectangles. Cut each one of them into thin strips of different widths of 1cm, 1.5 cm, and 3 cm. Use a tape and join the strips, end to end to make a belt. You should have three belts with different widths now. Find out the area and perimeters of each belt.
Belt 1 – Width 1 cm
Since the size of the rectangle is 14 cm x 9 cm, you will have 9 strips having a width of 1 cm and length of 14 cm. When you join the strips to make a belt, the total length of the belt is 14+14+14+14+14+14+14+14+14 = 126 cm. Hence, its perimeter = 2 (length + breadth) = 2 (126 + 1) = 2 x 127 = 254 cm. Its area = length x breadth = 126 x 1 = 126 square cm.
For Belt 1: Perimeter = 254 cm and Area = 126 square cm.
Belt 2 – Width 1.5 cm
Since the size of the rectangle is 14 cm x 9 cm, you will have 6 strips having a width of 1.5 cm and length of 14 cm. When you join the strips to make a belt, the total length of the belt is 14+14+14+14+14+14 = 84 cm. Hence, its perimeter = 2 (length + breadth) = 2 (84 + 1.5) = 2 x 85.5 = 171 cm. Its area = length x breadth = 84 x 1.5 = 126 square cm.
For Belt 2: Perimeter = 171 cm and Area = 126 square cm.
Belt 3 – Width 3 cm
Since the size of the rectangle is 14 cm x 9 cm, you will have 3 strips having a width of 3 cm and length of 14 cm. When you join the strips to make a belt, the total length of the belt is 14+14+14 = 42 cm. Hence, its perimeter = 2 (length + breadth) = 2 (42 + 3) = 2 x 45 = 90 cm. Its area = length x breadth = 42 x 3 = 126 square cm. For Belt 3: Perimeter = 90 cm and Area = 126 square cm.
Which belt is the longest? and Why?
Ans. Belt 1. Since its width is the smallest.
Why is the area of all the belts same?
Because the entire sheet of paper is used without any wastage.
How do you get a longer belt next time?
By reducing the width of the belt more.