1997 PMWC Problems/Problem I5
Problem
Two squares of different sizes overlap as shown in the given figure. What is the difference between the non-overlapping areas?
![[asy] import patterns; /* modified Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki, go to User:Azjps/geogebra */ import graph; usepackage("amsmath"); size(3.95cm); real labelscalefactor = 0.5; /* changes label-to-point distance */ pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ pen dotstyle = black; /* point style */ real xmin = -6.01, xmax = 15.94, ymin = -3.31, ymax = 13.18; /* image dimensions */ draw((3.94,4.18)--(6,5.09)--(6,6)--(3.14,6)--cycle); /* draw figures */ draw((0,0)--(0,6)); draw((0,0)--(6,0)); draw((0,6)--(6,6)); draw((6,6)--(6,0)); draw((2.33,7.85)--(3.94,4.18)); draw((2.33,7.85)--(5.99,9.45)); draw((5.99,9.45)--(7.6,5.79)); draw((7.6,5.79)--(3.94,4.18)); label("$ 6\text{cm} $",(-1.45,2.86),fontsize(15)); label("$ 4\text{cm} $",(8.46,7.95),fontsize(15)); add("crosshatch",crosshatch(.7mm)); fill((6,5.09)--(3.94,4.18)--(3.14,6)--(6,6)--cycle, pattern("crosshatch")); /* dots and labels */ clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); //Credit to dasobson for the diagram[/asy]](http://latex.artofproblemsolving.com/f/4/a/f4ae1ade0e1368e4ba4826e931762efd459554db.png)
Solution
Let the area of the non-shaded region of the 6 by 6 square by A. Let the area of the non-shaded region of the 4 by 4 square by B. Let the shaded area be C.
See Also
| 1997 PMWC (Problems) | ||
| Preceded by Problem I3 |
Followed by Problem I6 | |
| I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
