`A B C D` is a parallelogram. `P` is any point on `C Ddot` If `a r\ ( D P A)=15\ cm^2\ ` and `a r\ ( A P C)=20 c m^2,` then `a r\ ( A P B)=`
(a) `15 c m^2` (b) `20 c m^2` (c) `35\ c m^2` (d) `30 c m^2`

Explanation

In `|\|`gm ABCD, P is any point on CD

AP, AC and PB are joined.

area(`triangleDPA`)=`15cm^2`_____1

area(`triangleAPC`)=`20cm^2`__2

Now, Adding equation 1+2

ar(`triangleADC`)=`15+20`=`35cm^2`

`therefore` AC divides it into two triangle equal in area

area(`triangleACB`)=area(`triangleADC`)=`35cm^2`

...