Question

The given figure shows a parallelogram $ABCD$ with area $324c{m}^2$. $P$ is a point in $AB$ such that $AP:PB=1:2.$ Find the area of $△APD$.

• A. $34c{m}^2$
• B. $44c{m}^2$
• C. $24c{m}^2$
• D. $54c{m}^2$

Answer 1

The correct option is D $54c{m}^2$

If $DB$ is the diagonal,
Area of parallelogram $ABCD=2\times$area $△ADB=2\times$area $△BDC$
Area $△ADB=\frac{1}{2}\left(324\right)=162$
$P$ divides $AB$ in the ratio $1:2$ $(\frac{1}{3}:\frac{2}{3})$,
$\therefore$ Area $APD=\frac{1}{3}$ Area of $ADB=54$ sq. cm.