Geometry

ABCDEF is a regular hexagon and PQR is an equilateral triangle.

In ABCDEF, 

area(△AOB) = area(△BOC) = area(△COD) = area(△DOE) = area(△EOF) = area(△FOA) 

⇒area(ABCDEF) = area(△AOB + △BOC + △COD + △DOE + △EOF + △FOA) 

                            $= {\sqrt3 \over 4}+ {\sqrt3 \over 4}+ {\sqrt3 \over 4}+ {\sqrt3 \over 4}+ {\sqrt3 \over 4}+ {\sqrt3 \over 4}$

                            $=6× {\sqrt3 \over 4}$

                            $={3\sqrt3 \over 2}$ sq. units

⇒area(△PQR) $={\sqrt3 \over 4}×4$

                        $=\sqrt3$ sq. units

${area(ABCDEF)\over area(△PQR)} = {3\over 2} = 3:2$