Question

$\Delta PQR$ is formed by joining the midpoints of $\Delta ABC.$ Find the area of the $\Delta PQR$ if the area of the $\Delta ABC$ is $52c{m}^2$

• A. $26c{m}^2$
• B. $13c{m}^2$
• C. $18c{m}^2$
• D. $24c{m}^2$

Answer 1

The correct option is B

$13c{m}^2$

Since P and Q are mid-points of AB and BC,
APQR is a parallelogram.
PR is the diagonal of the parallelogram APQR, PR divides parallelogram APQR into two equal areas.
So, Area of $\Delta ARP=$ Area of $\Delta PRQ$
Similarly, Area of $\Delta PQB$ = Area of $\Delta PRQ$ and Area of $\Delta CRQ$ = Area of $\Delta PRQ$
So, Area of $\Delta PQR=\frac{1}{4}\times$ Area of $\Delta ABC=\frac{1}{4}\times 52=13c{m}^2$