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Question

ABCD ia a parallelogram. P is any point on CD. If ar (ΔDPA)=15 cm2 and ar (ΔAPC)=20 cm2, then find the ar (ΔAPB).


Your Answer
A
Your Answer
B
Correct Answer
C
Your Answer
D

Solution

The correct option is D
Given, P is any point on CD
ar (ΔDPA)=15 cm2
ar (ΔAPC)=20 cm2

AC is a diagonal of parallelogram ABCD, then
ΔADC=ΔABC ------(i)
We know, if parallelogram and triangle o the same base and between same parallels, the area of triangle is equal to half of the area of parallelogram.
ΔAPB and ΔACB are on same base AB and between same parallels.
So,  ar ΔAPB=ΔACB ----- (ii)
We know , from fig
ar (ΔACB)=ar (ΔAPD)+ar (ΔAPC)
from eq (2) and (3),
ar (ΔAPB)=15 cm2+20 cm2
ar (ΔAPB)=35cm2
Hence, correct option is  (c).

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