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4.7 Circles

Perimeter of a circle is the circumference which is given by the formula.

Perimeter of a circle = 2 p r where r is the radius, p = and has been discovered by ancient Greeks, by actually dividing the circumference of a circle by its diameter .

Area of a circle = p r2 where ' r ' is the radius of the circle.

Example 1

If the area of a square is 16 sqft. , find the length of each side .

Solution:

Area of a square = (length of one side)2

\ length of one side = 4 ft

Example 2

If the perimeter of a square = 24 inches , What is its area ?

Solution:

If perimeter 24 inches, length of each side = = 6 inches.

\ Area = (6 inches)2

= 36 square inches.

Example 3

The perimeter of a rectangle is 36 cm, find its area if the length of one side is 12 cm.

Solution:

Area = 72 cm2

Length of the rectangle = 12 and breadth = y

\ 2 ´ 12 + 2 y = 36

24 + 2y = 36

or 2y = 12

\y = 6 cm

Area = xy = 72 cm2

Example 4

The length of a rectangle is 10 cm and its perimeter is 30 cm. Find the area of this rectangle.

Solution:

Perimeter = 30 cm , length = 10 cm, breadth = y

2 ´ 10 + 2xy = 30

20 + 2y = 30

2y = 10

i.e. y = 5

\ area = 10 ´ 5

= 50

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Index

4.1 Perimeter
4.2 Square
4.3 Rectangle
4.4 Parallelogram
4.5 Triangle
4.6 Trapezoids
4.7 Circles

Chapter 5

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