Question

$ABCD$ is a parallelogram and P is the midpoint of $AB$. If $ar\left(APCD\right)=36c{m}^2$, find $ar\left(△ABC\right)$

• A. $36c{m}^2$
• B. $48c{m}^2$
• C. $24c{m}^2$
• D. $42c{m}^2$

Answer 1

Answer: (C)

$24c{m}^2$

Let $ABCD$ is a $\parallel$gm in which $AB=CD=2x$, then $AP=PB=x$, because $P$ is mid point. Draw $DE\perp AB=h$

or $APCD=36{cm}^2\Rightarrow \frac{1}{2}(x+2x)h=36⟶\left(1\right)$

ar $△ABC=\frac{1}{2}h\times 2x=hx⟶\left(2\right)$

$\frac{1}{2}\times 3x\times h=36\Rightarrow hx=24$(from eq(1))

Hence, ar $△ABC=hx=24{cm}^2$