2013 AMC 8 Problems/Problem 24: Difference between revisions
Chezbgone2 (talk | contribs) |
Chezbgone2 (talk | contribs) Added diagram. still needs shadiing |
||
| Line 3: | Line 3: | ||
<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 11:28, 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
