Question

In the given figure, $S$ and $T$ are the mid-points of sides $PR$ and $PQ$ respectively of $\Delta PQR$. If ar $\left(\Delta PQR\right)=48c{m}^2$, then find ar $\left(\Delta TSQ\right)$.

• A. $48c{m}^2$
• B. $24c{m}^2$
• C. $12c{m}^2$
• D. $6c{m}^2$

Answer 1

Answer: (C)

$12c{m}^2$

If area of $△PQR=48c.m^2$

If we consider $△QSP$, then

area of this triangle is $24c.m^2$

because QS is the median, median divide triangle in equal areas,

So, area of $△QSP=24c.m^2$

Now in $△QSP$ again 'ST' is median

So, area of $△QST=$ half of $△QSP=\frac{1}{2}ar\left(△QSP\right)$

$\therefore ar△QST=12c.m^2\to$ option$-$ C