The three medians of triangle ABC meet at G, and the area of triangle ABC is $48{\text{cm}}^2$. What is the area of triangle BGC?

The medians cut the triangle into six smaller triangles of equal area, and BGC is made of two of them, so it is 2/6 = 1/3 of the whole: $48/3=16{\text{cm}}^2$. A second route: with D the midpoint of BC, triangles GBC and ABC share the base BC while GD = ⅓ × AD, so the areas are in the ratio 1 : 3. The trap $24{\text{cm}}^2$ treats G as if it were the midpoint of the median — a median does halve the area, but G is not its midpoint — while $8{\text{cm}}^2$ is one of the six small pieces.