Ratio of the areas of two triangles using determinants

Given the triangle [i]ABC[/i]. Let the points E, F and G be the mid points of the sides of the triangle[i] ABC[/i] .[br]a) Find the ratio of the areas of the triangles [i] ABC[/i] and [i]EFG[/i] by exploring the Applet. [br]b) Prove by geometric means and by determinants.[br]c) Write your answer with algebraic notation in general terms.