in the figure, the diagonals of a quadrilateral split it into four triangles. the areas of three of them are shown in the picture ;
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A line from the vertex of a triangle divides the length of the opposite side and the area of triangle in the same ratio.
In ∆ ACD, a line DE is drawn from D to AC.
∴ AE : EC = Area ∆ AED : Area of ∆ CED
AE : EC = 60 : 30 = 2 : 1
In ∆ ACB, a line BE is drawn from B to AC.
∴ AE : EC = Area of ∆ AEB : Area of ∆ CEB
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