Olympiad Geometry · Challenge problem

Points $D$ and $E$ divide side $\overline{AB}$ of $\triangle ABC$ into three equal parts, with $D$ nearer to $A$. Lines through $D$ and $E$ parallel to $\overline{BC}$ cut the triangle into three pieces. The middle piece (between the two lines) has area $15$. Find the area of $\triangle ABC$.