2018 AMC 12A Problem 8

Problem 8 of 25EasierGeometry

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?

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Solution

The base

DE

\triangle ADE

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.

Tagged: similarity · power scaling of length, area, and volume