Difference between revisions of "2003 AMC 10B Problems/Problem 23"
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==Solution== | ==Solution== | ||
| − | + | Here is an easy way to look at this, where <math>p</math> is the perimeter, and <math>a</math> is the [[apothem]]: | |
Area of Octagon: <math> \frac{ap}{2}=1 </math>. | Area of Octagon: <math> \frac{ap}{2}=1 </math>. | ||
Revision as of 13:12, 29 December 2011
Problem
A regular octagon 
has an area of one square unit. What is the area of the rectangle 
?
![[asy] unitsize(1cm); defaultpen(linewidth(.8pt)+fontsize(8pt)); pair C=dir(22.5), B=dir(67.5), A=dir(112.5), H=dir(157.5), G=dir(202.5), F=dir(247.5), E=dir(292.5), D=dir(337.5); draw(A--B--C--D--E--F--G--H--cycle); label("$A$",A,NNW); label("$B$",B,NNE); label("$C$",C,ENE); label("$D$",D,ESE); label("$E$",E,SSE); label("$F$",F,SSW); label("$G$",G,WSW); label("$H$",H,WNW);[/asy]](http://latex.artofproblemsolving.com/5/0/e/50ef8af0ec716cfeea89017a030c7d57d3b40e4c.png)
Solution
Here is an easy way to look at this, where 
is the perimeter, and 
is the apothem:
Area of Octagon: 
.
Area of Rectangle: 
.
You can see from this that the octagon's area is twice as large as the rectangle's area is 
.
See Also
| 2003 AMC 10B (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 AMC 10 Problems and Solutions | ||
