Question

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

Answer: (B)

$\frac{1}{4}$th of the parallelogram PQRS

The required figure is attached in image.

Area of parallelogram = PQxAQ

Triangle OPQ have same base as that of parallelogram but height QB is half of height of parallelogram QA.

Area of triangle is half of PQxQB

=$\frac{PQ\ast QA}{4}$

=$\frac{1}{4}$ of area of parallelogram PQRS

So correct answer is Option B