Area of Rectangle

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.
Area of the rectangle ABCD = Total number of square boxes within rectangle
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

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.
rectangle ABCD of length 12 cm and breadth 6 cm
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.
rectangle ABCD of breadth 5 cm and diagonal 13 cm
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.
combined figure of rectangle and triangle
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.
rectangle of length 24 cm and breadth 14 cm
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


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