



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 = pr^{2}






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
= 4r^{2}






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 = pr^{2}






Example: 


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











copyright 2005 Bruce Kirkpatrick 
