Question 78947
please show me how to find the area of a regular hexagon with a perimeter of 100cm.
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Each side is 100/6 cm
Draw two consecutive line segments from the center
forming a triangle with the side.
The central angle is 360/6=60 degrees.
So the base angles are each 60 degrees also.
Draw the perpendicular bisector from the center
to the base.  Each of the small triangles is a 
60-30-90 rt triangle.  The side opposite the 
30 degree angle (half the side of the hexagon)
is half the hypotenuse. Knowing two of the sides
of the triangle you can find the altitude of the
60-60-60 triangle.  You can now find the area
of the 60-60-60 triangel.  Multiply that area
by six to get the area of the hexagon.
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Cheers,
Stan H.