Difference between revisions of "2008 AMC 10A Problems/Problem 21"
I like pie (talk | contribs) (Added problem, solution and image still needed) |
(Asymptote by worthawholebean (presumably)) |
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A cube with side length <math>1</math> is sliced by a plane that passes through two diagonally opposite vertices <math>A</math> and <math>C</math> and the midpoints <math>B</math> and <math>D</math> of two opposite edges not containing <math>A</math> or <math>C</math>, as shown. What is the area of quadrilateral <math>ABCD</math>? | A cube with side length <math>1</math> is sliced by a plane that passes through two diagonally opposite vertices <math>A</math> and <math>C</math> and the midpoints <math>B</math> and <math>D</math> of two opposite edges not containing <math>A</math> or <math>C</math>, as shown. What is the area of quadrilateral <math>ABCD</math>? | ||
− | + | <asy> | |
+ | import three; | ||
+ | unitsize(3cm); | ||
+ | defaultpen(fontsize(8)+linewidth(0.7)); | ||
+ | currentprojection=obliqueX; | ||
+ | |||
+ | draw((0.5,0,0)--(0,0,0)--(0,0,1)--(0,0,0)--(0,1,0),linetype("4 4")); | ||
+ | draw((0.5,0,1)--(0,0,1)--(0,1,1)--(0.5,1,1)--(0.5,0,1)--(0.5,0,0)--(0.5,1,0)--(0.5,1,1)); | ||
+ | draw((0.5,1,0)--(0,1,0)--(0,1,1)); | ||
+ | dot((0.5,0,0)); | ||
+ | label("$A$",(0.5,0,0),WSW); | ||
+ | dot((0,1,1)); | ||
+ | label("$C$",(0,1,1),NE); | ||
+ | dot((0.5,1,0.5)); | ||
+ | label("$D$",(0.5,1,0.5),ESE); | ||
+ | dot((0,0,0.5)); | ||
+ | label("$B$",(0,0,0.5),NW);</asy> | ||
<math>\mathrm{(A)}\ \frac{\sqrt{6}}{2}\qquad\mathrm{(B)}\ \frac{5}{4}\qquad\mathrm{(C)}\ \sqrt{2}\qquad\mathrm{(D)}\ \frac{5}{8}\qquad\mathrm{(E)}\ \frac{3}{4}</math> | <math>\mathrm{(A)}\ \frac{\sqrt{6}}{2}\qquad\mathrm{(B)}\ \frac{5}{4}\qquad\mathrm{(C)}\ \sqrt{2}\qquad\mathrm{(D)}\ \frac{5}{8}\qquad\mathrm{(E)}\ \frac{3}{4}</math> | ||
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==See also== | ==See also== | ||
{{AMC10 box|year=2008|ab=A|num-b=20|num-a=22}} | {{AMC10 box|year=2008|ab=A|num-b=20|num-a=22}} | ||
+ | |||
+ | [[Category:Introductory Geometry Problems]] |
Revision as of 11:29, 26 April 2008
Problem
A cube with side length is sliced by a plane that passes through two diagonally opposite vertices and and the midpoints and of two opposite edges not containing or , as shown. What is the area of quadrilateral ?
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
2008 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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 AMC 10 Problems and Solutions |