SOLUTION: Each side of a regular hexagon has length 10. Find the area of the hexagon. (Hint: Divide the Hexagon into triangles) How many triangles do I divide the hexagon into and what d

Algebra ->  Trigonometry-basics -> SOLUTION: Each side of a regular hexagon has length 10. Find the area of the hexagon. (Hint: Divide the Hexagon into triangles) How many triangles do I divide the hexagon into and what d      Log On


   



Question 109968: Each side of a regular hexagon has length 10. Find the area of the hexagon.
(Hint: Divide the Hexagon into triangles)
How many triangles do I divide the hexagon into and what do I do from there?
Or just write out the equation to solve it.
The answer in the answer key is 150 square roots of 3.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There are 6 equilateral triangles in a hexagon
Each one is 1/6 of the area
Area of a triangle = a
A+=+6a
a+=+%281%2F2%29bh
b = 10
The height is the perpendicular line that bisects one of the 60 degree
angles of the triangle. It divides the equilateral into two
triangles with sides in the ratio 1 : 2 : sqrt%283%29
In this case, the sides are 5:10:5%2Asqrt%283%29
a+=+%281%2F2%29bh
a+=+%281%2F2%2910%2A5%2Asqrt%283%29
a+=+25%2Asqrt%283%29
A+=+6a
A+=+6%2A25%2Asqrt%283%29
A+=+150%2Asqrt%283%29 answer