Difference between revisions of "2008 AMC 8 Problems/Problem 4"
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− | ==Problem== | + | == Problem == |
In the figure, the outer equilateral triangle has area <math>16</math>, the inner equilateral triangle has area <math>1</math>, and the three trapezoids are congruent. What is the area of one of the trapezoids? | In the figure, the outer equilateral triangle has area <math>16</math>, the inner equilateral triangle has area <math>1</math>, and the three trapezoids are congruent. What is the area of one of the trapezoids? | ||
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<asy> | <asy> | ||
size((70)); | size((70)); | ||
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draw((9.4,9.7)--(5.6,3.25)); | draw((9.4,9.7)--(5.6,3.25)); | ||
</asy> | </asy> | ||
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<math>\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 5 \qquad \textbf{(D)}\ 6 \qquad \textbf{(E)}\ 7</math> | <math>\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 5 \qquad \textbf{(D)}\ 6 \qquad \textbf{(E)}\ 7</math> | ||
− | ==Solution== | + | == Solution == |
The area outside the small triangle but inside the large triangle is <math>16-1=15</math>. This is equally distributed between the three trapezoids. Each trapezoid has an area of <math>15/3 = \boxed{\textbf{(C)}\ 5}</math>. | The area outside the small triangle but inside the large triangle is <math>16-1=15</math>. This is equally distributed between the three trapezoids. Each trapezoid has an area of <math>15/3 = \boxed{\textbf{(C)}\ 5}</math>. | ||
− | ==See Also== | + | == See Also == |
{{AMC8 box|year=2008|num-b=3|num-a=5}} | {{AMC8 box|year=2008|num-b=3|num-a=5}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 12:36, 19 October 2020
Problem
In the figure, the outer equilateral triangle has area , the inner equilateral triangle has area , and the three trapezoids are congruent. What is the area of one of the trapezoids?
Solution
The area outside the small triangle but inside the large triangle is . This is equally distributed between the three trapezoids. Each trapezoid has an area of .
See Also
2008 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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