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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