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# Area of a Regular Polygon?

I am not certain of my answers, and I would greatly appreciate if you could check them for me. Any help is great!

The question is what is the area of the regular polygon with the given radius or apothem? If your

Question 1) The first shape is a square with an apothem of 6. I figured that since the sides are equal each side equaled double the apothem and amounted to 12. Then I did 12*4 = 48. 48 * 48 = 2304, which made area = 2304 cm^2.

Question 2) The second shape is a hexagon with an apothem of 8* the square root of 3. To solve this I did 360 degrees divided by the 6 sides. Then tan(30 degrees) = x / 8 (square root of 3).

X = 8
8*2 = 16
96 * 8(square root of 3) = 1330.2
Area = 665.12 in.

Question 3) The third shape is another hexagon with an apothem of 6* the square root of three. To solve this I did 360 degrees divided by the 6 sides. Then tan(30 degrees) = x / 6 (square root of 3).
X = 6
6*2 = 12
72 * 6(square root of 3) = 748.3
Area = 374.1m