Geometry Calculating the Area of a Circle
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Round Area
Calculating the Area of a Circle

 

 Circles don't have sides.

 We can't use lengths and widths to calculate their areas.
 We don't know enough math yet to break a circle 
 into an infinite number of little triangles or donuts.
 
 All we can do for now
 is say what the formula for the area of a circle is
 

 Area of a Circle = p radius radius

 
 This is usually written as:
 

 Area of a Circle = pr2

 
 We can show you roughly why this is true.
 Draw a circle and put a square around it.
 

 

 
 Now draw 3 more radii (plural of radius)
 

 

 
 The area of each of these little squares
 is the radius times the radius, also known as r 2.
 There are 4 of these little squares, 
 so that makes the whole area:

 

 Area = 4r2

 
 The circle is some amount smaller 
 than this square we put around it.
 If you eyeball the parts that we need to leave out 
 around the edges of the square,
 it looks like a bit less than what we would need 
 to fill up one of the 4 squares.
 That means we need to subtract a bit less than 1
 from the 4 in the equation to get at the right answer.
 
 Just be estimating this, we can see that the number
 we need to multiply the r 2 by is a little bit more than 3.
 And pi is about 3.14159.
 
 This isn't really a proof, 
 we don't know enough math for that yet.
 What it is, is a "is that reasonable" test.
 
 In many situations, an "is that reasonable test" 
 is actually a lot more useful than a proof.
 
 So for now, you just have to accept it.
 The area of a circle is found by using the equation:
 

 Area of a Circle = pr2

 
 Example:
 Find the area of a circle with a radius of 3 ...
 

 

 

   copyright 2005 Bruce Kirkpatrick

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