2008 AMC 8 Problems/Problem 4

Problem

In the figure, the outer equilateral triangle has area $16$ , the inner equilateral triangle has area $1$ , and the three trapezoids are congruent. What is the area of one of the trapezoids?

$[asy] size((70)); draw((0,0)--(7.5,13)--(15,0)--(0,0)); draw((1.88,3.25)--(9.45,3.25)); draw((11.2,0)--(7.5,6.5)); draw((9.4,9.7)--(5.6,3.25)); [/asy]$

$\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 5 \qquad \textbf{(D)}\ 6 \qquad \textbf{(E)}\ 7$

Video Solution

https://www.youtube.com/watch?v=43JZqmiUeLw ~David

Solution

The area outside the small triangle but inside the large triangle is $16-1=15$ . This is equally distributed between the three trapezoids. Each trapezoid has an area of $15/3 = \boxed{\textbf{(C)}\ 5}$ .

Video Solution by OmegaLearn

https://youtu.be/abSgjn4Qs34?t=479

~ pi_is_3.14

2008 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2008 AMC 8 Problems/Problem 4

Contents

Problem

Video Solution

Solution

Video Solution by OmegaLearn

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