Problem 2

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Problem 2: (2018 AMC 10A, 9; 2018 AMC12A 8)

All of the triangles in the diagram below are similar to isosceles triangle $ABC$, in which $AB=AC$. Each of the $7$ smallest triangles has area $1,$ and $\triangle ABC$ has area $40$. What is the area of trapezoid $DBCE$?

$\textbf{(A) } 16 \qquad$ $ \textbf{(B) } 18 \qquad$ $ \textbf{(C) } 20 \qquad$ $ \textbf{(D) } 22 \qquad$ $ \textbf{(E) } 24$

Solution

Exercise 2: Solution

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 $DBCE$?

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