In \(\triangle ABC\), AD is a median and G is a point on AD such that AG : GD \(=2:1\). If the area of \(\triangle ABC\) is 36 cm2, what is the area of \(\triangle BDG\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6 cm2
A median splits a triangle into two triangles of equal area, since they have equal bases and the same height. Triangles with the same height have areas in the ratio of their bases.
D is the mid-point of BC, so area of \(\triangle ABD=\frac{1}{2}\times36=18\,\mathrm{cm^2}\)
\(\triangle BDG\) and \(\triangle ABD\) have the same height from B, with bases GD and AD
GD \(=\frac{1}{3}\)AD, so area of \(\triangle BDG=\frac{1}{3}\times18=6\,\mathrm{cm^2}\)
