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]

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.

$A+C=36$

$B+C=16$

$(A+C)-(B+C)=A-B=\boxed{20}$

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
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