If a hexagon is resting on a flat side, and has a total height of 18, what is the length of each side of the hexagon?
2007-10-26 14:13:23 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Hexagon is divided into 6 equal equilateral triangles. The altitude of triangle is given by sqrt(3) a/2, where a = side of hexagon.
The hexagon height = 2(altitude of of triangle)
2h = 18
2(sqrt(3) a/2) = 18
sqrt(3) a = 18
a = 18/sqrt(3) = 6 sqrt(3) units
2007-10-26 14:26:03 · answer #1 · answered by mohanrao d 7 · 0⤊ 0⤋
The interior angle of a hexagon is 120 so if you draw a straight line from the top of the hexagon down to the base, you will form a triangle that has a 30 degree angle (120 - rt angle) = 30 degree.
After that, it is just a trig property to determine the side of the hexagon. Half of the height (18/2 = 9) is one side of the triangle. The other side is the side of the hexagon with the enclose angle of 30 degrees.
cos(30) = 9/x
x=9/cos(30)
x=9/(sqrt(3)/2)
x=18/(sqrt(3))
x=10.39
2007-10-26 14:25:42 · answer #2 · answered by bustedtaillights 4 · 0⤊ 0⤋
Look at the hexagon as a collection of 6 equilateral triangles. I'd love to draw it here, but I cannot. Take the "bottom" triangle, draw a perpendicular bisector. Each half is a 30/60/90 degree triangle. The height of the triangle is side x SQRT(3)/2. So the height of the whole thing is side * sqrt (3).
So side * sqrt(3) = 18
side = 18/Sqrt(3) = 6 x 3 /sqrt(3) = 6 sqrt(3)
2007-10-26 14:28:59 · answer #3 · answered by Computer Guy 7 · 0⤊ 0⤋
18. i hope, if the hexagon is regular.
2007-10-26 14:23:38 · answer #4 · answered by Harris 6 · 0⤊ 0⤋