Difference between revisions of "2007 AMC 8 Problems/Problem 8"
(Created page with '== Problem == In trapezoid <math>ABCD</math>, <math>AD</math> is perpendicular to <math>DC</math>, <math>AD</math> = <math>AB</math> = <math>3</math>, and <math>DC</math> = <mat…') |
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<math>\triangle BEC</math>. | <math>\triangle BEC</math>. | ||
− | < | + | <asy> |
+ | defaultpen(linewidth(0.7)); | ||
+ | pair A=(0,3), B=(3,3), C=(6,0), D=origin, E=(3,0); | ||
+ | draw(E--B--C--D--A--B); | ||
+ | draw(rightanglemark(A, D, C)); | ||
+ | label("$A$", A, NW); | ||
+ | label("$B$", B, NW); | ||
+ | label("$C$", C, SE); | ||
+ | label("$D$", D, SW); | ||
+ | label("$E$", E, NW); | ||
+ | label("$3$", A--D, W); | ||
+ | label("$3$", A--B, N); | ||
+ | label("$6$", E, S);</asy> | ||
<math>\text{(A)}\ 3 \qquad \text{(B)}\ 4.5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 18</math> | <math>\text{(A)}\ 3 \qquad \text{(B)}\ 4.5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 18</math> | ||
− | |||
== Solution == | == Solution == | ||
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We are trying to find the area of <math>\triangle BEC</math>. | We are trying to find the area of <math>\triangle BEC</math>. | ||
− | So, <math>\frac{1}{2} | + | So, <math>\frac{1}{2} \cdot 3 \cdot 3 = \boxed{\textbf{(B)}\ 4.5}</math> |
+ | |||
+ | ==See Also== | ||
+ | {{AMC8 box|year=2007|num-b=7|num-a=9}} | ||
+ | {{MAA Notice}} |
Revision as of 01:24, 5 July 2013
Problem
In trapezoid , is perpendicular to , = = , and = . In addition, is on , and is parallel to . Find the area of .
Solution
We know that is a square with side length . We subtract and to get the length of .
We are trying to find the area of .
So,
See Also
2007 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.