Geometry Finding the Area of a Pentagon
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Finding the Area of a Pentagon

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 How could we find the area of a regular pentagon?

 
 
 OK, first what is a "regular" pentagon?
 Is there an irregular pentagon?
 
 A regular pentagon means that all of the sides 
 and angles are the same as each other.
 
 So say that we have this one ...
 
 
 What do we do?
 
 The first step is to cut up the pentagon
 kind of like a pizza.
 
 
 Now cut each of the pizza slices in half
 down the middle.
 
 
 Those last cuts go from the middle of each side
 to the middle of the pentagon.
 When we do that,
 we make 90 degree angles on each side.
 We also cut the length of each side
 exactly in half ...
 
 
 So now we have a bunch of little right triangles.
 Ten of them actually.
 Like this:
 
 
 So now if we were told the length of the other side,
 we would be in business!
 Say we are told it is about 4 (it's actually more like 4.1291).
 That means the area of each triangle is about:
 
 
 Or if we want to be more exact:
 
 
 There are 10 triangles in the pentagon, so
 
 
 Or to be more exact:
 
 
 So to solve the area of a regular pentagon, 
 we need to know two things.
 
 We need to know the length of a side.
 We need to know the length of a line
 from the middle of a side to the middle of the pentagon.
 
 Math types really like to make up special names for things.
 They made up a name for that middle of the side
 to middle of the shape line.
 They call it the APOTHEM, (yeesh! what a name ...)
 
 Example:
 Find the area of this pentagon ...
 
 

   copyright 2008 Bruce Kirkpatrick

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