Question

In figure, PQ || BC and PQ: BC = 1 : 3. If ar (ΔABC) = 144 cm², then ar (ΔAPQ) = ______.

Answer 1

In figure, PQ || BC and PQ: BC = 1 : 3. If ar (ΔABC) = 144 cm², then ar (ΔAPQ) = 16 cm².

Explanation:

Since PQ || BC, ΔAPQ ∼ ΔABC, so areas scale as the square of corresponding side ratio:

`(ar(APQ))/(ar(ABC)) = ((PQ)/(BC))^2` 

= `(1/3)^2`

= `1/9`

Hence ar(APQ) = `144 × 1/9`

= 16 cm²