All of the triangles in the diagram are similar to isosceles triangle $ABC$, in which $AB=AC$. Each of the $5$ smallest triangles immediately above $\overline{DE}$ has area $1$, and $\triangle ABC$ has area $45$. If $\overline{DE}$ (parallel to $\overline{BC}$) has length $3$ times the base of a smallest triangle, what is the area of trapezoid $DBCE$?

All the triangles are similar, so areas are proportional to squares of bases. Since $\overline{DE}$ spans $3$ bases of the smallest triangles, $[ADE]=3^2\cdot1=9$.
$[DBCE]=[ABC]-[ADE]=45-9=\boxed{36}$.