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Question

ABCD is a parallelogram. P is any point on CD. If ar(DPA) = 35 cm2 and ar(APC) = 15 cm2, then area(APB) is

A
15 cm2
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B
35 cm2
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C
50 cm2
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D
70 cm2
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Solution

The correct option is C 50 cm2

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


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