Difference between revisions of "2021 Fall AMC 12B Problems/Problem 15"
Lopkiloinm (talk | contribs) (→Solution) |
Lopkiloinm (talk | contribs) (→Solution) |
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| Line 18: | Line 18: | ||
label("C",C,N); | label("C",C,N); | ||
label("D",D,E); | label("D",D,E); | ||
| + | label("E",(0,3),W); | ||
| + | label("F",(3,0),E); | ||
</asy> | </asy> | ||
We can see that this shape is made out of <math>12</math> of these shapes. <math>\angle{A} = 30^{\circ}</math> and <math>\angle{C} = 90^{\circ}</math> | We can see that this shape is made out of <math>12</math> of these shapes. <math>\angle{A} = 30^{\circ}</math> and <math>\angle{C} = 90^{\circ}</math> | ||
Revision as of 16:01, 24 November 2021
Problem
Three identical square sheets of paper each with side length 
are stacked on top of each other. The middle sheet is rotated clockwise 
about its center and the top sheet is rotated clockwise 
about its center, resulting in the 
-sided polygon shown in the figure below. The area of this polygon can be expressed in the form 
, where 
, 
, and 
are positive integers, and is not divisible by the square of any prime. What is 
?
IMAGE
Solution
![[asy] pair A=(0,0); pair B=(1.732,3); pair C=(3,3); pair D=(3,1.732); draw(A--(0,3)--C--(3,0)--A, lightgray); draw(A--B--C--D--A); label("A",A,W); label("B",B,N); label("C",C,N); label("D",D,E); label("E",(0,3),W); label("F",(3,0),E); [/asy]](http://latex.artofproblemsolving.com/2/4/d/24d6518f0cf0e06db8dee1d8de5a2b78453f80c6.png)
We can see that this shape is made out of 
of these shapes. 
and 
