The diagram shows 3 identical regular hexagons with side length .7. If O_{1}, O_{2} O_{3} are their respective centers, what is the area of △O1O2O3?
The distance. D. from the center of any hexagon to its edge can ne found as
(1/2) side length / sin 30° = D /sin 60°
3.5 / (1/2) = D / (sqrt (3) / 2)
7 (sqrt (3) / 2 ) = D
The side of our triangle is twice this = 7sqrt (3)
So....O1O2O3 forms an equilateral triangle with a side length of 7sqrt (3)
It's area = (1/2) (7sqrt (3))^2 sqrt (3) / 2 = [ 147 sqrt (3) / 4 ] units^2