Question

In the adjoining figure there are two congruent regular hexagons each with side 6 cm.


What is the ratio of area of $\Delta BDF$ and $\Delta PQR$, if P, Q and R are the mid-points of side AF, BC and DE?

• A. 6 : 5
• B. 7 : 6
• C. 4 : 3
• D. 1 : 1

Answer 1

The correct option is C 4 : 3

Area of hexagon ABCDEF $=6\times \frac{\sqrt{3}}{4}\times (6{)}^2=54\sqrt{3}c{m}^2$
$\therefore$ Area of BDF $=\frac{1}{2}$ (Area of hexagon)
$=27\sqrt{3}c{m}^2$
Area of PQR =$\frac{\sqrt{3}}{4}\times \frac{9a^2}{4}$
$\frac{AreaBDF}{AreaPQR}$ = $\frac{4}{3}$