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MATH / Three squares each have sides of length 6 units and overlap each other as shown…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Three squares each have sides of length 6 units and overlap each other as shown below. The points where the sides cross are midpoints. Find the area of the gray figure in square units.

[asy]

size(3cm,3cm);

fill((0,1)--(1,1)--(1,2)--(0,2)--cycle,lightgray);
fill((0.5,0.5)--(1.5,0.5)--(1.5,1.5)--(0.5,1.5)
--cycle,lightgray);
fill((1,0)--(2,0)--(2,1)--(1,1)--cycle,lightgray);

draw((0,1)--(1,1)--(1,2)--(0,2)--(0,1));
draw((0.5,0.5)--(1.5,0.5)--(1.5,1.5)--(0.5,1.5)
--(0.5,0.5));
draw((1,0)--(2,0)--(2,1)--(1,1)--(1,0));

draw((-0.4,1)--(-0.4,2),Bars);
label("6",(-0.4,1.5),UnFill(1));

[/asy]

level

Level 3

type

Prealgebra

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Source and history

task_id
cf20b85b-5997-59b1-bfe6-6c8be857c39f
task_key
prealgebra--test--cf20b85b-5997-59b1-bfe6-6c8be857c39f
task_revision_id
1
config / split
prealgebra / test

Official source

initial import