Question

In Δ ABC , MN || BC .

If BC = 14 cm and MN = 6 cm , find `("Ar" triangle "AMN")/("Ar" . ("trapezium MBCN"))`

Answer 1

Δ AMN - Δ  ABC       {proved above in (a)}

`("Ar" triangle "AMN")/("Ar" triangle "ABC") = ("MN"/"BC")^2 = (6/14)^2 = 9/49`

`("Ar" triangle "AMN")/(("Ar" triangle "AMN") + "Ar" . ("trapezium MBCN")) = 9 / 49`

49 Ar. Δ AMN = 9 Ar. Δ AMN + 9 Ar .(trapezium MBCN) 

40 Ar. Δ AMN = 9 Ar.( trapezium MBCN) 

`("Ar" triangle "AMN")/("Ar" . ("trapezium MBCN")) = 9/40`