To determine any area of a shape we need to know the formula for the area of that particular shape which is for a regular hexagon is
Area of hexagon = (3 √3) a^2 / 2
where a is the length of the side of the hexagon
So, first, we determine the length of the side of the smaller hexagon from the given area.
3 in^2 = (3 √3) a^2 / 2
6 in^2 = (3 √3) a^2
a^2 = 2 √3 / 3
a = 1.0746 in
The length of the side of the bigger hexagon is twice that of the smaller so,
A = 2a = 2 (1.0746 in ) = 2.1491 in
Area of the bigger hexagon = (3 √3) a^2 / 2
= (3 √3) 2.1491^2 / 2 = 12 in^2
