Combined Figures





In this page combined figures we are going to see how to find the area and perimeter of combined geometric shapes. In our day to day life we see many combined shapes of triangle, rectangle,square and semi circle. To find the area and perimeter of such figures we need to calculate the area separately and then we can add them.

Example 1:

Find the perimeter and area of the following figures:

Solution:

In the above figure we have four semi circles and one square. To find the perimeter of the above figure we have to add the sum of four semicircles and a square.

Diameter of each semicircle is 7 cm from this we can find the radius of semi circle.

Radius = 7/2

        = 3.5 cm   

Length of each side of square = 7 cm

The perimeter of the given figure = 4 (perimeter of semicircles) +

                                          Perimeter of square

Perimeter of semi circle AEB = Π r

                                                = (22/7) x 3.5

                                                =  22 x 0.5

                                                =  11             

            Perimeter of 4 semi circles = 4 (11)

                                                = 44 cm

Perimeter of square = 4a

here a = 7 cm                      

                                       = 4 (7)                  

                                       = 28 cm

The perimeter of the given figure = 44 cm + 28 cm

                                       = 72 cm

Area of 1 semi circle = Π r²/2

                                             = (1/2) x (22/7) x (7/2)²

                                    = (1/2) x (22/7) x (7/2) x (7/2)

                                    = (1/2) x 11 x (7/2)

                                    = 77/4

                                    = 19.25 cm²

      Area of 4 semi circles = 4 (19.25)

                                   = 77

Area of square = a²

                             = (7)²

                             = 7 x 7

                             = 49 cm²

Area of given figure = Area of 4 semi circles + Area of square

                           = 77 + 49 

                           = 126 cm²  combined figures


Example 2:

Find the area of shaded portion.

Solution:

Area of shaded portion = Area of rectangle - Area of 4 quadrants of circle

Area of rectangle = L x W

Length of rectangle = 15 cm

Width of rectangle = 8 cm

                                  =  15 x 8

                                  =  120 cm²

Area of quadrant = Π r²/4

radius of quadrant = 3 cm

                                 = [(22/7) x 3²]/4       

                                 = (22 x 3 x 3)/(7 x 4)   

                                 = 198/28

Area of 4 quadrant = 4 x 198/28

                          = 198/7

                          = 28.28 cm²

Area of shaded portion = 120 - 28.28

                               = 91.715 cm²                              


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