what is the area of a regular hexagon with a side of 10 cm?

mbc4687

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1. what is the area of a regular hexagon with a side of 10 cm?
2. area of a regular heptagon with a side of7 inches?
 
hexagon is 6 sided
draw 2 lines from center of hexagon to each end of one side
the incuded angle is 360/6=60 degrees
draw a line perpindicular to the side at the midpoint of the side. This line passes through the center and is the altitude of the triangle formed by the side and the two lines drawn above
the tan 30degrees [ one half the included angle ] = 5 [ one half the side] / altitude
tan 30= 5/alt.
alt= 5 cot 30*

then the area of the triangle = 1/2 base x altitude
area of triangle = [1/2]5[5 cot 30*] there are 6 such triangles
area of hexagon = 6[1/2][25 cot 30*]
area of hexagon= 75 cot 30*

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the second figure is 7 sided and solved by the same manner

Arthur
 
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