2000 PMWC Problems/Problem I13

Problem

In the figure, the squares $ABCD$ and $DCEG$ both have the same area of $64cm^2$ . $EFG$ is a semicircle. The point $F$ is the mid-point of the arc $EFG$ . Find the area of the shaded part. (Assume $\pi=3.14$ )

$[asy] void unitsquare(pair p){ draw(p--(p.x+1,p.y)--(p.x+1,p.y+1)--(p.x,p.y+1)--cycle); return; } fill(buildcycle(arc((2,0.5),(2,0),(2,1)),(2,1)--(0,1)--(2.5,0.5)),gray); unitsquare((0,0)); draw((1,0)--(2,0)--(2,1)--(1,1)); draw(arc((2,0.5),(2,0),(2,1))); label("$A$",(0,1),NW); label("$B$",(0,0),SW); label("$C$",(1,0),S); label("$D$",(1,1),N); label("$E$",(2,0),S); label("$F$",(2.5,0.5),E); label("$G$",(2,1),N); //Credit to chezbgone2 for the diagram[/asy]$

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2000 PMWC Problems/Problem I13

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