# Area, Area and Area.

Geometry Level 5

In a $$\Delta ABC$$ D, E and F are mid-points of BC, AC and AB respectively. If P, Q, R are the points on AD, BE and CF such that $$\frac{AP}{AG} = \alpha$$, $$\frac{BQ}{BG} = \beta$$ and $$\frac{CR}{CG} = \gamma$$. Find area of $$\Delta PQR$$.

Given that $$G$$ is the centroid of $$\Delta ABC$$, $$\alpha = \frac{1}{2}$$, $$\beta = \frac{2}{3}$$, $$\gamma = \frac{3}{4}$$ and area of $$\Delta ABC = 4 \text{ unit}^2$$.

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