A polygon is a shape with straight edges that is closed all through out. When the number of sides get to 5 then it starts the shapes that end in gon. It goes the pentagon, then hexagon, then heptagon etc. You can only easily find the are of shapes that have sides that are all equivalent. You can find the area with the formula A=1/2ap. What does this mean exactly? The capital A stands for the area, the amount of square units in a given shape. The lowercase a stands for apothem. The apothem is the side of a regular polygon that is used in equations like this one. The p stands for perimeter, the linear units around the whole shape. So let's try this out. Let's say you have a heptagon with an apothem of 4. What is the area? Well first let's find the perimeter. So a short way to do it is multiply 4*7 because a heptagon has 7 sides and each side equals 4. The perimeter=28. Now we multiply this by the apothem, 4. That equals 118. But we are not done, we still have to multiply by 1/2. when we do it equals 59. This is how you find the area. If you found this helpful/interesting and if you have a request of what I should do next, feel free to comment.

I found this to be quite interesting, if only I had had this kind of formula for polygons when I was in gradeschool... You did a fine jjob of explaining the concept and giving an example. I am sure other users will find this useful when they come a cross it.

Normally for an octagon i just split it into 3 quadrilaterals and find the areas of those :p this way is less tedious

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hmm, this is interesting O: never knew this.

if only i could fully understand it though o: