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Area of a Circle

About 250 BC, the famous Greek mathematician Archimedes postulated that “the area of a circle is the same as the area of a triangle that has a base equal to the circumference of the circle and the height equal to the radius of the circle”. This is shown pictorially below:

area of circle=area of triangle

 

In that case, the area of the circle will become exactly equal to the area of the triangle. So

Area of circle A  =  {1/2}~*~base~*~height

  =  {1/2}~*~circumference~*~radius    circle with radius r

  =  {1/2}~*~2pi r~*~r

  =  pi r^2

So the area of a circle A is given by  A = pi r^2  

 

Example 1: What is the area of this circle?    circle with radius=7 cm

A = pi r^2

  = {22/7}~*~7~*~7

  = 154 cm2

 

Example 2: What is the area of the circle with diameter = 18 cm, correct to 1 decimal place? circle with diameter=18 cm

A = pi r^2

  = 3.14~*~9~*~9  (since r = 9)

  = 254.5 cm2

 

Example 3: Find (correct to 2 decimal places), the radius of a circle, whose area is 60 cm2?

A = pi r^2

60 = pi r^2, or

r2  = 60/pi

r  = sqrt{60/pi}

  = 4.37 cm