The lengths of the perpendiculars drawn to the sides of a regular hexagon from an interior point are 4, 5, 6, 8, 9, and 10 centimeters.
What is the number of centimeters in the length of a side of this hexagon?
Express your answer as a common fraction in simplest radical form.
With Aera A:
A=s2⋅sin(60∘)2⋅6|sin(60∘)=√32=s2⋅√322⋅6A=32√3s2
A=s⋅42+s⋅52+s⋅62+s⋅82+s⋅92+s⋅102=12(4+5+6+8+9+10)s=12⋅42sA=21s
s= ?
32√3s2=21s32√3s=21s=2123√3s=14√3s=14√3⋅√3√3s=143⋅√3
The number of centimeters in the length of a side of this hexagon is 143⋅√3 cm