Question

$ABCD$ is a parallelogram of area $162c{m}^2$. $P$ is a point on $AB$ such that $AP:PB=1:2$. Calculate the area of $\Delta APD$

• A. $20c{m}^2$
• B. $27c{m}^2$
• C. $24c{m}^2$
• D. $25c{m}^2$

Answer 1

The correct option is B $27c{m}^2$

If $DB$ is the diagonal,
Area of parallelogram $\frac{1}{2}ABCD=$ area $ADB=$ area $BDC$
Area ADB$=\frac{1}{2}\left(162\right)=81$
$P$ is mid point of $AB$ in the ratio $1:2$ $(\frac{1}{3}+\frac{2}{3})$

Area APD $=\frac{1}{3}\times$ Area of $ADB=\frac{1}{3}\left(81\right)=27$ sq. cm