Difference between revisions of "2016 AMC 8 Problems/Problem 22"

(Created page with "Rectangle <math>DEFA</math> below is a <math>3 \times 4</math> rectangle with <math>DC=CB=BA</math> The area of the "bat wings" is [asy] draw((0,0)--(3,0)--(3,4)--(0,4)--(0,0)...")
 
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Rectangle <math>DEFA</math> below is a <math>3 \times 4</math> rectangle with <math>DC=CB=BA</math> The area of the "bat wings" is
 
Rectangle <math>DEFA</math> below is a <math>3 \times 4</math> rectangle with <math>DC=CB=BA</math> The area of the "bat wings" is
[asy]
+
<asy>
 
draw((0,0)--(3,0)--(3,4)--(0,4)--(0,0)--(2,4)--(3,0));
 
draw((0,0)--(3,0)--(3,4)--(0,4)--(0,0)--(2,4)--(3,0));
 
draw((3,0)--(1,4)--(0,0));
 
draw((3,0)--(1,4)--(0,0));
 
fill((0,0)--(1,4)--(1.5,3)--(0,0), black);
 
fill((0,0)--(1,4)--(1.5,3)--(0,0), black);
 
fill((3,0)--(2,4)--(1.5,3)--(3,0), black);
 
fill((3,0)--(2,4)--(1.5,3)--(3,0), black);
[/asy]
+
</asy>
  
 
<math>\textbf{(A) }2\qquad\textbf{(B) }2 \frac{1}{2}\qquad\textbf{(C) }3\qquad\textbf{(D) }3 \frac{1}{2}\qquad \textbf{(E) }5</math>
 
<math>\textbf{(A) }2\qquad\textbf{(B) }2 \frac{1}{2}\qquad\textbf{(C) }3\qquad\textbf{(D) }3 \frac{1}{2}\qquad \textbf{(E) }5</math>

Revision as of 10:32, 23 November 2016

Rectangle $DEFA$ below is a $3 \times 4$ rectangle with $DC=CB=BA$ The area of the "bat wings" is

draw((0,0)--(3,0)--(3,4)--(0,4)--(0,0)--(2,4)--(3,0));
draw((3,0)--(1,4)--(0,0));
fill((0,0)--(1,4)--(1.5,3)--(0,0), black);
fill((3,0)--(2,4)--(1.5,3)--(3,0), black);
 (Error compiling LaTeX. /usr/local/share/asymptote/plain_picture.asy: 1234.11: runtime: non-cyclic path cannot be filled)

$\textbf{(A) }2\qquad\textbf{(B) }2 \frac{1}{2}\qquad\textbf{(C) }3\qquad\textbf{(D) }3 \frac{1}{2}\qquad \textbf{(E) }5$

Solution

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2016 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
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

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