Question

In the figure, the diagonals of a quadrilateral split it into four triangles. The areas of three of them are shown in the picture:

Calculate the area of the whole quadrilateral.

Answer 1

A line from the vertex of a triangle divides the length of the opposite side and the area of the 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
2 : 1 = Area of ∆AEB : 40
∴ Area of ∆ AEB = 40×2 = 80 sq.cm

∴ Total area of the quadrilateral = 60 + 30 + 80 + 40 = 210 sq.cm.