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Polygons, a la Shmoop. Farmer Polly at the Circle-P Farm needs to

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build some pens for her exotic animals.

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Polly doesn't want her animals to escape...

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...so she needs to build the animal pens in the shape of polygons.

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So what's a polygon?

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A polygon is any closed figure with three or more straight sides. "Closed" means that

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all sides connect together.

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There are no gaping holes in it that the three-toed sloth could escape through... very... slowly...

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These are not polygons: And no, a circle is not a polygon. It doesn't

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meet all the requirements... don't forget about the straight sides.

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Now these beauties, these are polygons. No animals are getting out of these bad boys.

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The last time the land octopus and the wallabies got out, Polly had a litter of eight-legged

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wallabies to round up.

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Those things can kick like you wouldn't believe. Unless you live in a circular cave, you've

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probably heard of triangles. Well, triangles are polygons with three sides.

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What do you call a polygon with four sides? A quadrilateral....

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Here are some key terms you should know: Angle: the shape formed when two rays meet

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at a common point.

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Vertex: the point where two rays meet; the corner point of a polygon. The plural

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of vertex is vertices....

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Side: the straight edge of a polygon. These are regular polygons...

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...called equilateral and equiangular, which means all sides are equal length and all angles

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are equal in measure.

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Since they're regular, Polly will put all the regular animals in here: the crocodiles,

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the giraffes, the fainting goats....

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Trust us, compared to the rest of these animals, the fainting goats are pretty regular.

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Now these suckers are not regular.

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There could be a few reasons:

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All sides are not equal.

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All angles are not equal.

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All sides and all angles are not equal. Nothing's equal. Not a thing.

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This is where Polly will put those eight-legged kangaroos, the flying sloth, and the talking

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donkey.

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He's such a smart... well, let's just say he has quite a mouth on him.

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Finally, there are convex and concave polygons. A convex polygon has no angles pointing inwards.

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More precisely, no internal angles can be more than a hundred eighty degrees.

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...So basically what the fence looks like when the bull moose gets angry.

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If there are any internal angles greater than a hundred eighty degrees, then the polygon

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is concave. Now you're ready to help Farmer Polly out

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on the farm.

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Don't worry, you won't have to milk the bovine-ocerus until you learn about volume and cylinders...

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