Difference between revisions of "2007 AMC 8 Problems/Problem 12"
(Created page with 'if the equalateral triangles are squased into the hexagon, it would fit perfectly! so the answer is '''1:1 or A'''') |
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| − | + | ==Problem== | |
| + | A unit hexagram is composed of a regular hexagon of side length <math>1</math> and its <math>6</math> | ||
| + | equilateral triangular extensions, as shown in the diagram. What is the ratio of | ||
| + | the area of the extensions to the area of the original hexagon? | ||
| + | |||
| + | <center>[[Image:AMC8_2007_12.png]]</center> | ||
| + | |||
| + | <math>\mathrm{(A)}\ 1:1 \qquad \mathrm{(B)}\ 6:5 \qquad \mathrm{(C)}\ 3:2 \qquad \mathrm{(D)}\ 2:1 \qquad \mathrm{(E)}\ 3:1</math> | ||
| + | |||
| + | ==Solution== | ||
| + | The six equilateral triangular extensions fit perfectly into the hexagon meaning the answer is <math>\boxed{\textbf{(A) }1:1}</math> | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2007|num-b=11|num-a=13}} | ||
Revision as of 23:41, 12 November 2012
Problem
A unit hexagram is composed of a regular hexagon of side length 
and its 
equilateral triangular extensions, as shown in the diagram. What is the ratio of
the area of the extensions to the area of the original hexagon?
Solution
The six equilateral triangular extensions fit perfectly into the hexagon meaning the answer is 
See Also
| 2007 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 | ||
