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How could we find the area of a regular pentagon? |
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| 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 ... | ||||||||
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| What do we do? | ||||||||
| The first step is to cut up the pentagon | ||||||||
| kind of like a pizza. | ||||||||
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| Now cut each of the pizza slices in half | ||||||||
| down the middle. | ||||||||
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| 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 ... | ||||||||
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| So now we have a bunch of little right triangles. | ||||||||
| Ten of them actually. | ||||||||
| Like this: | ||||||||
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| 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: | ||||||||
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| Or if we want to be more exact: | ||||||||
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| There are 10 triangles in the pentagon, so | ||||||||
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| Or to be more exact: | ||||||||
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| 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 ... | ||||||||
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copyright 2008 Bruce Kirkpatrick |
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