opposite sides of a regular hexagon are 12cm apart. the length of each sidein cm is
Answers
take the hexagon and draw diagonals through each of the opposite corners.
this breaks the hexagon up into 6 equilateral triangles.
each of the sides of these equilateral triangles will be 12 inches long.
area of a triangle is 1/2 base * height.
we have the base.
we need the height.
take one of the equilateral triangles and drop a perpendicular from opposite side.
this becomes the height of the triangle.
the right triangles become 30-60-90 triangles.
in a 30-60-90 triangle, the sides opposite the angles are in the following ratio:
side opposite 30 degrees = .5
side opposite 60 degrees = sqrt%283%29%2F2
side opposite 90 degrees = 1
height is side opposite 60 degrees.
base is side opposite 30 degrees.
since the base is (1/2)*L and the hypotenuse equals L, the height is equal to
sqrt%283%29%2F2*L
-----
we now have enough to compute the area of the hexagon.
-----
area of the hexagon is 6 * the area of each equilateral triangle.
area of each equilateral triangle is 1/2 * base * height.
base = 12
height = sqrt%283%29%2F2*12
formula becomes
6 * (1/2) * 12 * sqrt%283%29%2F2*12
answer is:
374.1229744.
-----
thanks