Difference between revisions of "2009 AMC 8 Problems/Problem 7"
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\textbf{(D)}\ 6 \qquad | \textbf{(D)}\ 6 \qquad | ||
\textbf{(E)}\ 9</math> | \textbf{(E)}\ 9</math> | ||
| + | |||
| + | ==Solution== | ||
| + | The area of a triangle is <math>\frac12 bh</math>. If we let <math>CD</math> be the base of the triangle, then the height is <math>AB</math>, and the area is <math>\frac12 \cdot 3 \cdot 3 = \boxed{\textbf{(C)}\ 4.5}</math>. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2009|num-b=6|num-a=8}} | {{AMC8 box|year=2009|num-b=6|num-a=8}} | ||
Revision as of 15:29, 25 December 2012
Problem
The triangular plot of ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. HOw many square miles are in the plot of land ACD?
![[asy] size(250); defaultpen(linewidth(0.55)); pair A=(-6,0), B=origin, C=(0,6), D=(0,12); pair ac=C+2.828*dir(45), ca=A+2.828*dir(225), ad=D+2.828*dir(A--D), da=A+2.828*dir(D--A), ab=(2.828,0), ba=(-6-2.828, 0); fill(A--C--D--cycle, gray); draw(ba--ab); draw(ac--ca); draw(ad--da); draw((0,-1)--(0,15)); draw((1/3, -1)--(1/3, 15)); int i; for(i=1; i<15; i=i+1) { draw((-1/10, i)--(13/30, i)); } label("$A$", A, SE); label("$B$", B, SE); label("$C$", C, SE); label("$D$", D, SE); label("$3$", (1/3,3), E); label("$3$", (1/3,9), E); label("$3$", (-3,0), S); label("Main", (-3,0), N); label(rotate(45)*"Aspen", A--C, SE); label(rotate(63.43494882)*"Brown", A--D, NW); [/asy]](http://latex.artofproblemsolving.com/5/b/3/5b3fa3817ad8d7032d6357d1446ffb5cfec46ac6.png)
Solution
The area of a triangle is 
. If we let 
be the base of the triangle, then the height is 
, and the area is 
.
See Also
| 2009 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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 | ||
