Area of Composite Figure


 
 
Concept Explanation
 

Area of Composite Figure

A figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape). The area of a composite figure is calculated by dividing the composite figure into basic figures and then using the relevant area formula for each basic figure.

Illustration: Find the area of the following composite figure:

Solution: The figure can be divided into a rectangle and triangle as shown:

  

So, the area of the composite figure is large 216cm^2

Illustration: Find the area of the shaded region.

Solution:

Given: Side of the outer square = 10 cm

Area of outer square = Side X Side

                                      = 10 X 10

                                      = 100 sq cm

Given: Side of the square which lies in the interior of above diagram = 1 cm

Area of the square which lies in the interior of the above diagram = Side X Side

                                                                                                                     = 1 X 1

                                                                                                                      = 4 sq cm

As 4 squares lie in the interior region, Hence the sum of the area of all the 4 squares = 4 + 4 + 4 + 4

                                                                                                                                               = 16 sq cm

Now, area of shaded region = Area of the outer square - Area of 4 interior squares         

                                                   = 100 - 4

                                                    = 96 sq cm

Illustration:  A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.

Solution: Area of the rectangular floor = length X breadth

                                                                   =  5 X 4

                                                                  = small 20;m^{2}

and the area of square carpet = side X side

                                                        = 3 X 3

                                                       = small 9;m^{2}

The area of the floor that is not carpeted = Area of the rectangular floor  -   area of square carpet

                                                                         = (20 - 9) sq m

                                                                        = small 11;m^{2}

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Find the area of the shaded region in the following figure

Right Option : D
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Explanation
Question : 2

Find the area of the following composite figure:

Right Option : C
View Explanation
Explanation
Question : 3

Find the area of the figure shown below

Right Option : A
View Explanation
Explanation
 
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