Two similar regular hexagons have a common center. If each side of the big hexagon is twice the side of the small one and the area of the small hexagon is 3 sq. in, what is the area of the big hexagon?

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