Centroid

The three medians divide the triangle into six smaller triangles, with the same area. The yellow triangle's sides are the one-thrid of each median. If the area of the $ABC$ triangle is a, then the area of the yellow triangle is $\dfrac{1}{2}*\dfrac{1}{6}a=\dfrac{1}{12}a.$

So there always exist a triangle, the sides of which are the one-third of each median of a triangle. The area of this, smaller triangle is one-twelfth of the larger triangle's area.

If a triangle's sides are $3, 4$ and $5$ , then it is a right-angled triangle, and its area is $\dfrac{3*4}{2}=6$ . If we zoom out this triangle to its one-third, then we get the sought triangle, and its area is $1.5$ . Therefore the big triangle's area is $12*1.5=\boxed{18}$ .