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.

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

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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°

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.

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.

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.