Given ΔABC∼ΔPQR, if AB/PQ = 1/3, then find ar(ΔABC)/ar(ΔPQR).

Let AD be the perpendicular dropped from A to the side BC and PS be the perpendicular dropped from P to the side QR respectively.
Since, ΔABC∼ΔPQR, we have ΔABD∼ΔPQS.
Therefore, AB/PQ = AD/PS = BC/QR ⇒ ar(ΔABC)/ar(ΔPQR) = (AD × BC)/(PS × QR) = (AB/PQ) × (AB/PQ) = (AB/PQ)² = (1/3)² = 1/9