Question

In ΔPQR, PM and QN are medians. Area of ΔGQM = 15 cm². Find the area of ΔPQR.

Answer 1

Given 

• ar(ΔGQM) = 15 cm²
• And PM and QN are medians.

Therefore, PG : GM = 2 : 1 (Medians of a Δ intersect in the ratio 2 : 1)

Now, ΔPQG and ΔGQM lie on the same base PM and have a common vertex Q. 

So, heights are same.

`(ar(ΔPQG))/(ar(ΔGQM)) = (1/2 xx PG xx h)/(1/2 xx GM xx h)`

`(ar(ΔPQG))/15 = (PG)/(GM)`

`(ar(ΔPQG))/15 = 2/1`

ar(ΔPQG) = 30 cm²

Since the median of a triangle divides it into two triangles of equal areas.

Therefore, ar(ΔPQR) = 2 × ar(ΔPQM)

= 2 × ar(ΔPQG) + ar(ΔGQM)

= 2 × 30 + 15

= 2 × 45

= 90 cm²