Area of Rectangle

Area of Rectangle

Area is the region covered by the plane figure. Rectangle is a four sided plane figure having its opposite sides equal and each angle 90°. Area of rectangle is measured by the product of its length and breadth.

Let ABCD be a rectangle 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 rectangle ABCD = Total number of square boxes within rectangle.

                                              = No. of squares along the length × No. of squares along the breadth

                                              = 5 × 3

                                              = 15

Since each square box have the area 1 cm²

Area of the rectangle ABCD = 15 × 1 cm²

                                             = 15 cm²

∴  Area of a rectangle = length (l)×breadth (b) = l×b

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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 rectangle.

Solution: Here,

                                Length of the rectangle (l) = 12cm

                                Breadth of the rectangle (b) = 6cm

                                ∴  Area of rectangle (A) = l × b

                                                                        = 12cm × 6cm

                                                                        = 72cm²

Example 2: Find the area of the given rectangle.

Solution: Here,

                                Length of the diagonal (d) = 13cm

                                Breadth of the rectangle (b) = 5cm

                                We know,

                                               l² + b² = d²

                                or,          l² + 5² = 13²

                                or,          l² + 25 = 169

                                or,          l² = 169 – 25

                                or,          l² = 144

                                 

       

          

                                ∴  Area of rectangle (A) = l × b

                                                                        = 12cm × 5cm

                                                                        = 60cm²

Example 3: If the length of a rectangle is double of its breadth and its perimeter is 30m, find its length, breadth and area.

Solution: Let,

                                Breadth of the rectangle (b) = x

                                ∴  Length of the rectangle (l) = 2x

                                Perimeter of the rectangle  = 30m

                                i.e.          2(l + b) = 30m

                                or,          2(2x + x) = 30

                                or,          2 × 3x = 30

                                or,          6x = 30

                                or,          x = 30/6

                                or,          x = 5m

                ∴  Length of the rectangle (l) = 2x = 2 × 5m = 10m

                Breadth of the rectangle (b) = x = 5m

                

                Area of the rectangle = l × b

                                                     = 10m × 5m

                                                     = 50m²

Example 4: Find the area of the given combined figure.

Solution: Here,

                                Length of the rectangular surface (l) = 20m

                                Breadth of the rectanglular surface (b) = 14cm

                                ∴  Area of rectangular part (A₁) = l × b

                                                                                      = 20cm × 14cm

                                                                                      = 280cm²

                Again,

                                Base of triangular surface (b) = 14cm

                                Height of triangular surface (h) = 10cm

                               

                                                                                           

                                                                                 = 70cm²

                          

                           ∴  Total area of the given figure = A₁ + A₂

                                                                                 = 280cm² + 70cm²

                                                                                 = 350cm²

Example 5: Find the area of the shaded region given in the figure.

Solution: Here,

                                Length of the rectangle (l) = 24m

                                Breadth of the rectangle (b) = 14cm

                                ∴  Area of rectangle (A₁) = l × b

                                                                          = 24cm × 14cm

                                                                          = 336cm²

                Again,

                                Length of square (l) = 10cm

                                ∴  Area of triangular part (A₂) = l²

                                                                                   = (10cm)²

                                                                                   = 100cm²

                                ∴  Area of the shaded region = A₁ –  A₂

                                                                                  = 336cm² – 100cm²

                                                                                  = 236cm²

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