Area of Composite Figure
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
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
=
and the area of square carpet = side X side
= 3 X 3
=
The area of the floor that is not carpeted = Area of the rectangular floor - area of square carpet
= (20 - 9) sq m
=
The area of a square of side 8 cm is the same as that of a rectangle of length 32 cm. What is the breadth of the rectangle? | |||
| Right Option : B | |||
| View Explanation | |||
The diagonals of a quadrilateral is 25 m in length and the perpendiculars to it from the opposite vertices are 8.4 m and 12 m . Find the area of the quadrilateral. | |||
| Right Option : A | |||
| View Explanation | |||
Find the area of the shaded region.
| |||
| Right Option : C | |||
| View Explanation | |||
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