# A park in the shape of a hexagon has a fence that is 24 m long. What is the area of the park.

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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))

= s^2*sqrt(3)/4

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**