# 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.

$A+C=36$

$B+C=16$

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