Question

In $\triangle ABC$, points P, Q and R are the mid-points of sides AB, BC and CA respectively. If area of $\triangle ABC$ is 20 sq. units, find the area of $\triangle PQR$.

• A. 10 sq. units
• B. $5\sqrt{3}$ sq. units
• C. 5 sq. units
• D. None of these

Hint:

The medial triangle formed by joining midpoints of a triangle’s sides always has $\frac14$ the area of the original.

Answer 1

The Correct Option is C

P, Q, R are midpoints of the sides, so $\triangle PQR$ is the medial triangle of $\triangle ABC$. The medial triangle’s area is always $\frac{1}{4}$ of the original triangle’s area. Thus, Area$(PQR) = \frac{1}{4} \times 20 = 5$ sq. units.