Area of Square

Area of Square

Area of Square

Area is the region covered by the plane figure. A square is a four sided plane figure having its all sides equal and each angle 90°. Area of square is measured by the product of its length and length i.e. length square.
Area of the square ABCD = Total number of square boxes within the square ABCD
Let ABCD be a square and it is divided into unit squares of side 1cm each and hence the area of each square is 1 cm2.
Now,
Area of the square ABCD = Total number of square boxes within the square ABCD.
                                          = No. of squares along horizontal length × No. of squares along vertical breadth
                                          = 3 × 3
                                          = 9
Since each square box have the area 1 cm2
Area of the square ABCD = 9 × 1 cm2
                                          = 9 cm2
  Area of a square = length (l) × length (l) = l × l = l2

Area of square in terms of diagonal

Diagonals of a square are equal and they bisect to each other at 90°. Let ABCD be the square and AC and BD are diagonals (d). Since diagonals are equal and they bisect to each other at 90°
Square ABCD
Area of square in terms of diagonal

Note: Area is measured in square units. For example cm2, mm2, m2 etc. are the units of area.


Workout Examples

Example 1: Find the area of the given plane figure.
square of length(l) = 6cm
Solution: Here,
                                The given figure the square of length(l) = 6cm
                                Area of square = l2
                                                          = (6cm)2
                                                          = 36cm2


Example 2: Find the area of the given square.
square ABCD with diagonal AC = 5√2 cm
area of square = 1/2 × d^2


Example 3: If the perimeter of a square garden is 160m, find its area and cost of paving its floor at Rs 200 per square meter.
Solution: Here,
                                Perimeter of square garden = 160m
                                i.e.          4l = 160m
                                or,           l = 160/4
                                or,          l = 40m
                               
                                ∴  Area of square = l2
                                                              = (40m)2
                                                              = 1600m2
                                
                                Rate of paving floor = Rs. 200/m2
                               
                                ∴  Cost of paving = Rate × Area
                                                              = Rs. 200 × 1600
                                                              = Rs. 320000


You can comment your questions or problems regarding the area of square here.

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