1. **Problem statement:** Given an isosceles triangle $ABC$ with $AB=AC$ and area 40, inside which there are 7 smallest similar triangles each with area 1, find the area of trapezoid $DBCE$. 2. **Understanding the problem:** All smaller triangles are similar to $ABC$, so their areas scale by the square of the similarity ratio. 3. **Key formula:** If two triangles are similar with similarity ratio $r$, then their areas relate by $r^2$. 4. **Step-by-step solution:** - The 7 smallest triangles each have area 1, so total area of these 7 is 7. - The large triangle $ABC$ has area 40. - The trapezoid $DBCE$ is formed by removing the 7 smallest triangles from $ABC$ and possibly some other parts. - Since the 7 smallest triangles sum to area 7, the remaining area in $ABC$ is $40 - 7 = 33$. - The trapezoid $DBCE$ is exactly the part of $ABC$ excluding the 7 smallest triangles. 5. **Final answer:** $$\boxed{33}$$