2018 AMC 12A Problem 8

Below is the professionally curated solution for Problem 8 of the 2018 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 12A solutions, or check the answer key.

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Difficulty rating: 1440

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 $DBCE?$

$16$

$18$

$20$

$22$

$24$

Solution:

The base $DE$ of $\triangle ADE$ is $4$ times the base of a smallest triangle, so by the square scaling of similar areas, $[ADE] = 4^2 \cdot 1 = 16.$ The trapezoid $DBCE$ is what remains of $\triangle ABC,$ so its area is $40 - 16 = 24.$

Thus, the correct answer is E.

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