Answer:
150 sqrt 3 = 259.8076 units^2
Explanation:
Interior angles of hexagon = 120 degrees ....now look at the Right 1/2 of the hexagon... see illustration....this is a trapezoid...
One base is 10 units
the other labelled 'base' is
10 cos 60 + 10 cos 60 + 10 = 20 units
the height of this trapezoid is 10 sin 60 = 10 * sqrt(3)/2 = 5 sqrt(3)
the area of this trapezoid is then 1/2 ( 10+ 20) * 5 sqrt (3) = 75 sqrt 3
there are TWO of these trapezoids in the hexagon so total area is then
2 * 75 sqrt 3
150 sqrt 3