In the given figure, ABCDEF is a regular hexagon of side 12 cm P, Q and R are the mid points of the sides AB, CD and EF respectively. What is the area (in cm2) of triangle PQR?

In the given figure, ABCDEF is a regular hexagon of side 12 cm P, Q and R are the mid points of the sides AB, CD and EF respectively. What is the area (in cm²) of triangle PQR?

Answer: Option B

Solution

Answer: Option B

Solution:

So, If
OF = OE = ED
So, FC = 24 cm
So, RQ $$=\frac{\text{FC}+\text{ED}}{2}=\frac{36}{2}$$
RQ = 18 cm
Area of $$\Delta \text{PQR}=\frac{\sqrt{3}}{4}\times 18\times 18=81\sqrt{3}\text{ c}{\text{m}}^2$$