Question

The diagonals of a quadrilateral split it into four triangles. The area of three of them are given. Area of triangle apb=60^2, area of triangle cpd=30cm^2, area oftriangle cpb=40cm^2.calculate the whole area of ABCD

Answer 1

Answer:

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 = 2 : 1

∴ Area of ∆ AEB =  40 × 20 1 40×201 = 80 sq.cm

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