Maths / Areas Of Parallelograms And Triangles / Relation between Area of Parallelogram and Triangle

QUESTION

ABCD is a parallelogram. P is any point on CD. If $ar(\Delta DPA)=15\;cm^2$ and  $\large ar(\Delta PBC)=20\;cm^2$, then $ar(\Delta APB)=$

 OPTIONS A. $15\;cm^2$ B. $20\;cm^2$ C. $35\;cm^2$ D. $30\;cm^2$
Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

$ar(\Delta DPA)=15\;cm^2$ and  $\large ar(\Delta PBC)=20\;cm^2$

Through p draw a line PQ || AD

AQPD is a parallelogram and AP is the diagonal

$\large ar(\Delta APQ)=ar (\Delta DPA)=15\;cm^2$

PCBQ is a parallelogram and PB is the diagonal

$\large ar(\Delta PBQ)=ar (\Delta PBC)=20\;cm^2$

, then $ar(\Delta APB)= ar(\Delta AQP ) + ar (\Delta BQP )= 20 + 15 = 35 cm^2$

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