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Area of a Square

As we know, a square is a special type of rectangle, in that all the four sides of the square are of same and equal length.

The area of a square with a side of ‘s’ units is given by the formula

A = s x s

A = s2

Let us look at the following three squares. The first square has a side equal to 3 cm, the second has a side 2 cm long, and the last square has a side 4 cm long. Dividing each square with unit lines (here 1 cm each) will give us smaller squares within the ‘big’ square. Adding all these ‘small’ squares will give us the total area of the square.

                                        area of square with side=3 cm

Area = 3 x 3  =  9 cm2     

  

 

                                         area of square with side=2 cm

Area = 2 x 2  =  4 cm2          

  

                                         area of square with side=4 cm

Area = 4 x 4  =  16 cm2    

 

 

 

Mathematically speaking, the area of a square is obtained by multiplying the number of squares along the length by the number of squares along the breadth. In other words, we could square the number of squares along one side to obtain the area of the square.

 

Example 1: What is the area of a square with side 6 cm?

Area A = s2

  =  6 x 6

  =  36 cm2

 

Example 2: What is the length of the side of a square with area 49 cm2?

Area A = s2          area of square=49 sq cm

49  =  k2

k  =  sqrt{49}

   =  7 cm

 

In the next section, we look at calculating the area of a rectangle, and then some examples of calculating area of composite shapes containing squares and rectangles