ABCD is a parallelogram. P is any point on CD. If ar(△DPA) = 35 cm2 and ar(△APC) = 15 cm2, then area(△APB) is
Given: ABCD is a parallelogram.
area(△DPA) = 35 cm2
area(△APC) = 15 cm2
To find: area(△APB)
Area(ΔACD)=Area(ΔDPA)+Area(ΔAPC)
=35cm2+15cm2
=50cm2
Now, ABCD is a parallelogram.
AC is the diagonal of parallelogram ABCD.
A diagonal of a parallelogram divides it into two congruent triangles.
⇒ Area(△ACD)=Area(△ACB) =50 cm2
△ACB and △APB are on same base AB and between same parallels AB and DC.
Hence,
Area(ΔAPB)=Area(ΔACB)
=50 cm2