Difference between revisions of "2021 Fall AMC 10B Problems/Problem 19"

(Created page with "== Problem == Three identical square sheets of paper each with side length <math>6{ }</math> are stacked on top of each other. The middle sheet is rotated clockwise <math>30^...")
 
(Problem)
Line 1: Line 1:
 
== Problem ==
 
== Problem ==
  
Three identical square sheets of paper each with side length <math>6{ }</math> are stacked on top of each other. The middle sheet is rotated clockwise <math>30^\circ</math> about its center and the top sheet is rotated clockwise <math>60^\circ</math> about its center, resulting in the <math>24</math>-sided polygon shown in the figure below. The area of this polygon can be expressed in the form <math>a-b\sqrt{c}</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are positive integers, and <math>c</math> is not divisible by the square of any prime. What is <math>a+b+c?</math>
 
  
https://d2fr23tawm9iun.cloudfront.net/images/contests/00301-0c73c4b87027afe833e737ee22eee4251f7ac624/files/2021-AMC10B-q18-fig.png
+
==See Also==
 
+
{{AMC10 box|year=2021 Fall|ab=B|num-a=20|num-b=18}}
<math>(\textbf{A})\: 75\qquad(\textbf{B}) \: 93\qquad(\textbf{C}) \: 96\qquad(\textbf{D}) \: 129\qquad(\textbf{E}) \: 147</math>
+
{{MAA Notice}}

Revision as of 00:52, 23 November 2021

Problem

See Also

2021 Fall AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 18
Followed by
Problem 20
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png