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MATH / The area of square ABCD is 100 square centimeters, and AE=2 cm. What is the area of square EFGH, in square centimeters? [asy] pair a,b,c,d,e,f,g,h; a=(0,17); b=(17,17); c=(17,0); d…

Problem

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

problem

The area of square ABCDABCD is 100 square centimeters, and AE=2AE = 2 cm. What is the area of square EFGHEFGH, in square centimeters? [asy] pair a,b,c,d,e,f,g,h; a=(0,17); b=(17,17); c=(17,0); d=(0,0); e=(5,17); f=(17,12); g=(12,0); h=(0,5); label("AA",a,N); label("BB",b,N); label("CC",c,S); label("DD",d,S); label("EE",e,N); label("FF",f,E); label("GG",g,S); label("HH",h,W); draw(a--b--c--d--cycle); draw(e--f--g--h--cycle); [/asy]
Plain-text mathematical notation (without MathML)
The area of square ABCD is 100 square centimeters, and AE=2 cm. What is the area of square EFGH, in square centimeters?

[asy]
pair a,b,c,d,e,f,g,h;
a=(0,17);
b=(17,17);
c=(17,0);
d=(0,0);
e=(5,17);
f=(17,12);
g=(12,0);
h=(0,5);
label("A",a,N);
label("B",b,N);
label("C",c,S);
label("D",d,S);
label("E",e,N);
label("F",f,E);
label("G",g,S);
label("H",h,W);
draw(a--b--c--d--cycle);
draw(e--f--g--h--cycle);
[/asy]
Original LaTeX notation
The area of square $ABCD$ is 100 square centimeters, and $AE = 2$ cm. What is the area of square $EFGH$, in square centimeters?

[asy]
pair a,b,c,d,e,f,g,h;
a=(0,17);
b=(17,17);
c=(17,0);
d=(0,0);
e=(5,17);
f=(17,12);
g=(12,0);
h=(0,5);
label("$A$",a,N);
label("$B$",b,N);
label("$C$",c,S);
label("$D$",d,S);
label("$E$",e,N);
label("$F$",f,E);
label("$G$",g,S);
label("$H$",h,W);
draw(a--b--c--d--cycle);
draw(e--f--g--h--cycle);
[/asy]

level

Level 2

type

Geometry

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Source and history

task_id
42a8241d-95be-5f26-8615-f607b369aa0b
task_key
geometry--test--42a8241d-95be-5f26-8615-f607b369aa0b
task_revision_id
1
config / split
geometry / test

Official source

initial import