ABCD is a parallelogram. P is any point on CD. If ar(△DPA) = 35 cm2 and ar(△

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ABCD is a parallelogram. P is any point on CD. If ar( $△$ DPA) = 35 $c m^{2}$ and ar( $△$ APC) = 15 $c m^{2}$ , then area( $△$ APB) is

Options:

A . 15

c m^{2}

B . 35

c m^{2}

C . 50

c m^{2}

D . 70

c m^{2}

Answer: Option C
:
C

Given: ABCD is a parallelogram.
area( $△$ DPA) = 35 $c m^{2}$
area( $△$ APC) = 15 $c m^{2}$
To find: area( $△$ APB)
$A r e a (Δ A C D) = A r e a (Δ D P A) + A r e a (Δ A P C)$
$= 35 c m^{2} + 15 c m^{2}$
$= 50 c m^{2}$
Now, ABCD is a parallelogram.
AC is the diagonal of parallelogram ABCD.
A diagonal of a parallelogram divides it into two congruent triangles.
$\Rightarrow A r e a (△ A C D) = A r e a (△ A C B) = 50 c m^{2}$
$△ A C B$ and $△ A P B$ are on same base AB and between same parallels AB and DC.
Hence,
$A r e a (Δ A P B) = A r e a (Δ A C B)$
$= 50 c m^{2}$

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