The area of a square is given by the formula width time's height. But since the square has all the sides equal, the height is of the same measure as its width. Hence its formula is given by side times side. If s is the measure of one side of a half times, product of diagonals, square, then its area can be written as A= s x s = s²
If we know the measure of the diagonal of the square then the area is given by half times the product of the diagonals. But in a square since the diagonals are equal, the formula for area can be written as half times d times d which can be written as A= ½[dxd] = ½ (d²). The unit for area is always measured in square units.
The adjacent figure represents a square whose side is s and the diagonal is d. s d
Now let us consider a problem for example:
1. Find the area of a square whose side is 5cm.
Since the side is given as 5cm, A= sxs = 5x 5 = 25 sq cm.
2. Find the area of a square whose diagonal is given as 6 cm.
The area of square given diagonal is = ½ (d²) = ½ [6x6]
= 36/2 =18sqcm.