Regular hexagon is made of 6 equilateral triangles.

Perimeter of hexagon is 6 sides of a small △
Perimeter of bigger △ is 3 sides of it.

Since you're given 1 : 2,

6 small sides : 3 big sides = 1 : 2

6 small sides × 2 = 3 big sides

12 small sides = 3 big sides

1 big side = 4 small sides

Ratio of 1 small △ side : 1 big △ side
= 1 : 4

Both are equilateral △ so they are similar.


Area ratio of 1 small △ to 1 big △

= 1² : 4²
= 1 : 16


Area of 6 small △ (which is area of one hexagon) : area of big△

= 6 : 16
= 3 : 8

Or simply, divide the number for the hexagon by 6 and the one for the triangle by 3.


Ratio of side of small △: side of big △

= (1÷6) : (2÷3)

= 1/6 : ⅔
= 1 : 4
(Multiply both by 6)


Ratio of area of 1 small △ : 1 big △
= 1² : 4²
= 1 : 16


Ratio of hexagon area : △

= (6×1) : 16
= 6 : 16
= 3 : 8