Question

In the figure AP:PB=1:2 and PQ:QC=1:2. 1)what part of area of triangle ABC is the area of triangle APC? 2)what part of the area of the triangle ABC is the area of triangle AQC?

Answer 1

If a point divides a side in m:n, then the line joining the opposite vertex and the point divides the area of triangle in m:n. Hence proved that area of triangle AQC :area of triangle ABC=2:5.

Answer 2

If a point divides a side in m:n, then the line joining the opposite vertex and the point divides the area of triangle in m:n. Hence proved that area of triangle AQC :area of triangle ABC=2:5.