Question

In PQRS is a parallelogram. If L, M are the midpoints of QR and PS respectively, and O is any point on LM, then the area of triangle OPQ is equal to

• A. $\frac{1}{3}$ rd of the parallelogram PQRS
• B. $\frac{1}{4}$ th of the parallelogram PQRS
• C. $\frac{1}{2}$ of the parallelogram PQRS
• D. $\frac{1}{6}$ th of the parallelogram PQRS

Answer 1

The correct option is B $\frac{1}{4}$ th of the parallelogram PQRS

Consider the parallelogram as drawn above.

We know that the area of the triangle is $A=\frac{1}{2}\times b\times h$ where $b$ and $h$ are the base and height of the triangle respectively.

Therefore, area of $△POQ$ is:

$A=\frac{1}{2}\times PQ\times OD=\frac{1}{2}PQ\times \frac{1}{2}DB=\frac{1}{2}(PQ\times DB)=\frac{1}{4}\left(Ar\right(PQRS\left)\right)$

Hence, the area of $△OPQ$ is equal to $\frac{1}{4}$th of the parallelogram $PQRS$.