Difference between revisions of "2013 AMC 8 Problems/Problem 24"
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<math> \textbf{(A)}\hspace{.05in}\frac{1}{4}\qquad\textbf{(B)}\hspace{.05in}\frac{7}{24}\qquad\textbf{(C)}\hspace{.05in}\frac{1}{3}\qquad\textbf{(D)}\hspace{.05in}\frac{3}{8}\qquad\textbf{(E)}\hspace{.05in}\frac{5}{12}</math> | <math> \textbf{(A)}\hspace{.05in}\frac{1}{4}\qquad\textbf{(B)}\hspace{.05in}\frac{7}{24}\qquad\textbf{(C)}\hspace{.05in}\frac{1}{3}\qquad\textbf{(D)}\hspace{.05in}\frac{3}{8}\qquad\textbf{(E)}\hspace{.05in}\frac{5}{12}</math> | ||
| + | |||
| + | <asy> | ||
| + | pair A,B,C,D,E,F,G,H,I,J; | ||
| + | A = (0.5,2); | ||
| + | B = (1.5,2); | ||
| + | C = (1.5,1); | ||
| + | D = (0.5,1); | ||
| + | E = (0,1) | ||
| + | F = (0,0); | ||
| + | G = (1,0); | ||
| + | H = (1,1); | ||
| + | I = (2,1); | ||
| + | J = (2,0); | ||
| + | draw(A--B); | ||
| + | draw(C--B); | ||
| + | draw(D--A); | ||
| + | draw(E--I); | ||
| + | draw(F--E); | ||
| + | draw(I--J); | ||
| + | draw(J--F); | ||
| + | draw(G--H); | ||
| + | draw(A--J); | ||
| + | label("$A$", A, NW); | ||
| + | label("$B$", B, NE); | ||
| + | label("$C$", C, NE); | ||
| + | label("$D$", D, NW); | ||
| + | label("$E$", E, NW); | ||
| + | label("$F$", F, SW); | ||
| + | label("$G$", G, S); | ||
| + | label("$H$", H, N); | ||
| + | label("$I$", I, NE); | ||
| + | label("$J$", J, SE); | ||
| + | </asy> | ||
==Solution== | ==Solution== | ||
Revision as of 12:28, 27 November 2013
Problem
Squares 
, 
, and 
are equal in area. Points 
and 
are the midpoints of sides 
and 
, respectively. What is the ratio of the area of the shaded pentagon 
to the sum of the areas of the three squares?
pair A,B,C,D,E,F,G,H,I,J;
A = (0.5,2);
B = (1.5,2);
C = (1.5,1);
D = (0.5,1);
E = (0,1)
F = (0,0);
G = (1,0);
H = (1,1);
I = (2,1);
J = (2,0);
draw(A--B);
draw(C--B);
draw(D--A);
draw(E--I);
draw(F--E);
draw(I--J);
draw(J--F);
draw(G--H);
draw(A--J);
label("$A$", A, NW);
label("$B$", B, NE);
label("$C$", C, NE);
label("$D$", D, NW);
label("$E$", E, NW);
label("$F$", F, SW);
label("$G$", G, S);
label("$H$", H, N);
label("$I$", I, NE);
label("$J$", J, SE);
(Error making remote request. Unknown error_msg)
Solution
See Also
| 2013 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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. 
