Difference between revisions of "2007 AMC 8 Problems/Problem 23"
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| + | ==Problem== | ||
What is the area of the shaded pinwheel shown in the <math>5 \times 5</math> grid? | What is the area of the shaded pinwheel shown in the <math>5 \times 5</math> grid? | ||
<asy> | <asy> | ||
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<math> \textbf{(A)}\: 4\qquad\textbf{(B)}\: 6\qquad\textbf{(C)}\: 8\qquad\textbf{(D)}\: 10\qquad\textbf{(E)}\: 12 </math> | <math> \textbf{(A)}\: 4\qquad\textbf{(B)}\: 6\qquad\textbf{(C)}\: 8\qquad\textbf{(D)}\: 10\qquad\textbf{(E)}\: 12 </math> | ||
| + | ==Solution== | ||
| + | The area of the square around the pinwheel is 25. The area of the pinwheel is equal to the square - the white space. There are four triangles which have a total area of 15, and there are four white corner squares. Therefore the area of the pinwheel is <math>25-(15+4)</math> which is <math>\boxed{\textbf{(B) 6}\6}</math> | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2007|num-b=22|num-a=24}} | {{AMC8 box|year=2007|num-b=22|num-a=24}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 12:39, 25 July 2013
Problem
What is the area of the shaded pinwheel shown in the 
grid?
![[asy] filldraw((2.5,2.5)--(0,1)--(1,1)--(1,0)--(2.5,2.5)--(4,0)--(4,1)--(5,1)--(2.5,2.5)--(5,4)--(4,4)--(4,5)--(2.5,2.5)--(1,5)--(1,4)--(0,4)--cycle, gray, black); int i; for(i=0; i<6; i=i+1) { draw((i,0)--(i,5)); draw((0,i)--(5,i)); }[/asy]](http://latex.artofproblemsolving.com/f/c/c/fccd411afd0b28b0f07e081eeb90439e7ff3c2b9.png)
Solution
The area of the square around the pinwheel is 25. The area of the pinwheel is equal to the square - the white space. There are four triangles which have a total area of 15, and there are four white corner squares. Therefore the area of the pinwheel is 
which is $\boxed{\textbf{(B) 6}\6}$ (Error compiling LaTeX. Unknown error_msg)
See Also
| 2007 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
| 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. 
