Area and Perimeter of Rectangles and Squares

1. Perimeter of Rectangle

square metre or square meter
The perimeter of a rectangle is the length of all its 4 sides. This can be represented using a model as below.
square metre or square meter
Perimeter  =  Length  +  Breadth  +  Length  +  Breadth
=  2  ×  Length  +  2  ×  Breadth

square metre or square meter
Length  +  Breadth  =  Perimeter  ÷  2

Perimeter of Rectangle  =  2  ×  Length  +  2  ×  Breadth

2. Perimeter of Square

square metre or square meter
All sides of a square are equal.
Perimeter  =  Length  +  Length  +  Length  +  Length
=  4  ×  Length

Perimeter of Square  =  4  ×  Length

3. Area of Rectangle and Square

Let's find the area of the rectangle below.
square metre or square meter
To find the area of the rectangle, we find out how many one-centimetre squares we can fit into the rectangle.
square metre or square meter

Area of the rectangle  =  4  ×  2
 =  8 cm2

We need 8 one-centimetre squares to make a rectangle 4 cm long and 2 cm wide.
The area of the rectangle is 8 cm2.


Area of Rectangle  =  Length  ×  Breadth

Area of Square  =  Length  ×  Length


4. Find the area and perimeter of a rectangle with a length of 6 cm and a breadth of 4 cm.

square metre or square meter
Area  =  Length  ×  Breadth
 =  6  ×  4
 =  24 cm2

Perimeter  =  2  ×  Length  +  2  ×  Breadth
 =  2  ×  6  +  2  ×  4
 =  12  +  8
 =  20 cm

5. A square table cloth has a side of 5 m. What are its perimeter and area?

square metre or square meter
Area  =  5  ×  5
 =  25 m2

Perimeter  =  4  ×  5
 =  20 m

6. A 4 m long rectangular mat has an area of 12 m2.
a)  What is its breadth?
b)  What is its perimeter?

square metre or square meter
a)   Area        =  Length  ×  Breadth
      Breadth  =  Area  ÷  Length
 =  12  ÷  4
 =  3 m

b)   Perimeter  =  2  ×  Length  +  2  ×  Breadth
 =  ( 2  ×  4 )  +  ( 2  ×  3 )
 =  8  +  6
 =  14 m

7. Monty joins 4 identical straws to form a square of area 144 cm2.
What is the perimeter of the square formed?

square metre or square meter
Area of Square  =  Side  ×  Side
144  =  12  ×  12
Side  =  12 cm

Perimeter  =  4  ×  Side
 =  4  ×  12
 =  48 cm

8. The figure below is made of Rectangle A and Square B. Find the area and perimeter of the figure.

square metre or square meter
Area of Rectangle A  =  14  ×  3
=  42 cm2

Area of Square B  =  7  ×  7
=  49 cm2

Area of Figure  =  42  +  49
 =  91 cm2

Perimeter of Figure  =  14  +  3  +  4  +  7  +  7  +  7  +  3  +  3
 =  48 cm

9. All lines in the figure below meet at right angles. Find the area and perimeter of the figure.

square metre or square meter
Perimeter of Figure  =  12 + 50 + 14 + 50 + 14 + 25 + 14 + 25 + 14 + 50 + 14 + 50 + 12 + 70
 =  414 cm


square metre or square meter
Area of Figure  =  Area of A  +  Area of B  +  Area of C  +  Area of D
=  (70 × 12)  +  (50 × 14)  +  (25 × 14)  +  (50 × 14)
=  840  +  700  +  350  +  700
2590 cm2

10. Carlos mounts his painting on a frame as shown below.
a)   Find the perimeter of the painting.
b)   Find the area of the painting.
c)   Find the area of the border of the frame.

square metre or square meter
a) Length of painting  =  82 cm  −  11 cm  −  11 cm
 =  60 cm

    Breadth of painting  =  72 cm  −  6 cm  −  16 cm
 =  50 cm

    Perimeter of painting  =  2  ×  Length of painting  +  2  ×  Breadth of painting
 =  (2 × 60 cm)  +  (2 × 50 cm)
 =  120 cm  +  100 cm
 =  220 cm

b) Area of painting  =  Length of painting  ×  Breadth of painting
 =  60 cm  ×  50 cm
 =  3000 cm2

c) Area of frame  =  82 cm  ×  72 cm
 =  5904 cm2

    Area of border  =  Area of frame  −  Area of painting
 =  5904  −  3000
 =  2904 cm2

11. The figure below shows wooden tiling around a swimming pool.
a)   Find the perimeter of the figure.
b)   Find the area of the pool.
c)   Find the area of the tiling.

square metre or square meter
a) Length of big rectangle  =  50 cm  +  25 m  +  50 cm
 =  100 cm  +  25 m
 =  1 m  +  25 m
 =  26 m

    Breadth of big rectangle  =  50 cm  +  15 m  +  50 cm
 =  100 cm  +  15 m
 =  1 m  +  15 m
 =  16 m

    Perimeter of figure  =  Perimeter of big rectangle
 =  (2 × 26 m)  −  (2 × 16 m)
 =  52 m  −  32 m
 =  20 m
100 cm = 1 m
b) Area of pool  =  Area of small rectangle
 =  25 m  ×  15 m
 =  375 m2

c) Area of tiling  =  Area of big rectangle  −  Area of small rectangle
 =  (26 m  ×  16 m)  −  375 m2
 =  416 m2  −  375 m2
 =  41 m2