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You can find the area of any regular polygon with this equation: 1/2ap where a is the apothem and p is the perimeter.

To find the perimeter, multiply 7 times 12 to get 84.

To find the apothem, divide 360 (the amount of degrees around the center of the polygon) by 7 (the amount of sides you have) to get about 51.43. This gives you the measure of the angle of one triangle connected to 2 adjacent vertices. You have to make this a right triangle so that you can use trigonometry to find the apothem, so divide that angle by 2 to get 25.72. You know the side opposite of this angle is 6 because it is half the amount of the side (remember we divided this triangle by 2). To find the apothem at this point, use trigonometry. tan25.72 = 6/x. The apothem is 12.46.

So, plug all of this into your calculator; a = 1/2(84)(12.46). You find the area to be about 523.3.

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Q: Find the area of a regular 7-gon with a side length of 12?
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