A park in the shape of a hexagon has a fence that is 24 m long. The area of the park has to be determined.
Assuming that the hexagon is a regular one with all sides of the same length, it has 6 sides with the same length. As the fence around the park is 24 m long, each side has a length equal to 24/6 = 4 m.
The area of a regular hexagon with side a is `3*sqrt 3*a^2/2`
Substituting a = 4
=> `3*sqrt 3*4^2/2`
=> `3*sqrt 3*16/2`
=> `24*sqrt 3` m^2
The area of the park is `24*sqrt 3` m^2
The length of fence = perimeter of the hexagonal park = 24 m
One side of the park = 24/6 = 4m
A regular hexagon can be divided in to 6 equilateral triangles with sides equal to the side of the hexagon - say "s".
Area of the equilateral triangle = (1/2)*s*(s/2*tan(60))
The area of the park = 6 times the area of equilateral triangle with sides equal to 4m
The area of park = 6*4^2*sqrt(3)/4 = 24*sqrt(3) = 41.57 m2
Area of the hexogonal park is 41.57 sqaure meters