Area and Its Boundary

Area of Rectangles and Squares

The area of a rectangle or square is the amount of surface covered by it. On the other hand, the perimeter is the length of the total boundary of the figure. Today we will look at how to calculate the area of a rectangle and square.

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Area of a Rectangle and Square

Ram and Rohini purchased dried mango slices from a shop. After coming out of the shop, they started comparing who got a bigger piece? Their pieces looked like these:

area of a rectangle

Not being able to find the answer they approached a friend – Shiv. He gave them the idea of using small squares to calculate the area. So, Ram and Rohini cut square pieces of paper of side 1 cm. Then, they started measuring the pieces of the dried mango slices.

Ram managed to place 30 small squares on his piece and Rohini had 33 pieces. Finally, their question was answered. Rohini had the bigger piece. However, Ram looked a little interested in the squares. He observed that the total number of squares that fit on his piece was equal to the multiplication of the measurement of both sides. (5cm x 6cm = 30 square cm).

Similarly, he observed that in Rohini’s case it was 11cm x 3 cm = 33 square cm. Hence, he thought that it would be simpler to multiply both sides of a rectangle or square to find its area.

Exercise 1

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:

  1. What is its area?
  2. 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.

Solved Examples for You

Question: Draw a square of 9 square cm. Write ‘A’ on it. Draw another square with double the side. Write a ‘B’ on it.

area of a rectangle

Answer these —

  1. The perimeter of square A is __________ cm.
  2. The side of square B is __________ cm.
  3. The area of square B is __________ square cm.
  4. The area of square B is __________ times the area of square A.
  5. The perimeter of square B is __________ cm.
  6. The perimeter of square B is __________ times the perimeter of square A.

Solution:

  1. The perimeter of square A is ________. Since the area of square A = 9 cm, the length of its side = 3 cm (3 x 3 = 9). Hence, the perimeter of square A = 4 x length of side = 4 x 3 = 12 cm.
  2. The side of square B = 2 x 3 = 6 cm.
  3. The area of square B = length x breadth = 6 x 6 = 36 square cm.
  4. The area of square B is ____________ time the area of square A. We know that the area of square B is 36 square cm. And, the area of square A = 9 square cm. Hence, the area of square B is 4 times the area of square A.
  5. The perimeter of square B = 4 x length of side = 4 x 6 = 24 cm.
  6. The perimeter of square B is ________ time the perimeter of square A. We know that the perimeter of square B is 24 cm and square A is 12 cm. Hence, the perimeter of square B is 2 times the perimeter of square A.
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