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Assume regular hexagon of side L.

Split the hexagon into 6 equilateral triangles. (A sketch would help here)

You need to find the height of the triangle to find it's area.

Split the triangle in half with a vertical line.

You now have 2 right angle triangles of base L/2 height h. Top angle 30 degrees, bottom angle 60 degrees.

L/(2h) = tan 30

h = L/(2tan 30)

h = root 3 L/2

Area of 1 equilateral triangle = 1/2 x L x h

= (root 3 x L2)/4

Area of hexagon = 6x(root 3 x L2)/4

Area of hexagon = 3x(root 3 x L2)/2

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Q: Can you prove that area formula of hexagon?
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