Problem: Find the area of a regular hexagon whose sides measures 5 cm
Sol'n 1: I can cut the hexagon into 6 small triangles, so the area of triangle times 6 will be equal to the area of the polygon. Since the triangles are equilateral I can use the formula for it.
Area of triangle = $\frac{\sqrt{3}}{4}(5)^2= 10.83$
Area of hexagon = (6)(10.83) = 64.95
Sol'n 2: Using the formula $\frac{1}{2}(base)(height)$ for the area of triangle. The angle of triangle (angle at the radius) is equal to 60 degrees (From 360 / 6). Cutting the triangle into half (to get the base and height) will result to an angle of 30 degrees and base of 2.5.
To get the height: $tan(30) = \frac{2.5}{height} = 4.33$, so the area of the triangle: $\frac{1}{2}(2.5)(4.33) = 5.41$
Area of hexagon = (6)(5.41) = 32.475 which does not equal to the area in solution 1.
Question: I noticed that the area calculated on solution 2 is half the area calculated in solution 1. I don't know why. I don't think plugging in the original length of the base is right or logical? I have answered a related problem like this and I have gotten the polygon's area with 1/2(base)(height) and not plugging the original base length back to the formula of area after getting the height. Topic is easy but I don't get why I get so confused. :( Any help will be appreciated.