Question

A regular hexagon has sides of 3 feet. What is the area of the hexagon?

https://media.glynlyon.com/g_geo_2012/13/img_geou13a_64.gif

27 ft^2
18 ft^2
9 ft^2
13.5 ft^2

Answer 1

\[a ^{2}=3^{2}-\left( \frac{ 3 }{ 2 } \right)^{2}=9-\frac{ 9 }{ 4 }=9\left( 1-\frac{ 1 }{4 } \right)=9*\frac{ 3 }{ 4 }\]
\[a=\frac{ 3\sqrt{3} }{2 }\]
\[area of \triangle=\frac{ 1 }{2 }*3*\frac{ 3\sqrt{3} }{2 }=\frac{ 9\sqrt{3} }{4 }\]
\[Area of hexagon=6*\frac{ 9\sqrt{3} }{4 }=\frac{ 27\sqrt{3} }{2 }\]