Question

In the adjoining figure $DP$ is parallel to $AC$, then the ratio of area of triangle $PCB$ and quadrilateral $ABCD$ is

• A. $1:1$
• B. $1:2$
• C. $1:4$
• D. $2:3$

Answer 1

The correct option is A $1:1$

$\Delta PCB=\Delta PCA+\Delta CABandABCD=\Delta DCA+\Delta CAB$
Here, we observe that $\Delta CAB$ is common in both the triangle PCB and quadrilateral ABCD. So, we can say, a triangle on the same base and between the same parallels have the same area.
Hence ratio of the area of $\Delta PCB$ and quadrilateral ABCD is $1:1$.