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MATH / In the figure below, ABDC, EFHG, and ASHY are all squares; AB=EF=1 and AY=5. What is the area of quadrilateral DYES? [asy] size(5cm); defaultpen(black+1); pair a=(0,5); pair b=(1,5…

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problem

In the figure below, ABDC,ABDC, EFHG,EFHG, and ASHYASHY are all squares; AB=EF=1AB=EF =1 and AY=5AY=5. What is the area of quadrilateral DYESDYES? [asy] size(5cm); defaultpen(black+1); pair a=(0,5); pair b=(1,5); pair c=(0,4); pair d=(1,4); pair e=(4,1); pair f=(5,1); pair g=(4,0); pair h=(5,0); pair y=(0,0); pair s=(5,5); draw(a--s--h--y--a); draw(c--d--b,gray); draw(g--e--f,gray); draw(d--y--e--s--d); dot(a); dot(b); dot(c); dot(d); dot(e); dot(f); dot(g); dot(h); dot(y); dot(s); label("AA",a,NW); label("BB",b,N); label("CC",c,W); label("DD",d,SE); label("EE",e,NW); label("FF",f,E); label("GG",g,S); label("HH",h,SE); label("YY",y,SW); label("SS",s,NE); [/asy]
Plain-text mathematical notation (without MathML)
In the figure below, ABDC, EFHG, and ASHY are all squares; AB=EF=1 and AY=5.

What is the area of quadrilateral DYES?

[asy]
size(5cm);
defaultpen(black+1);
pair a=(0,5); pair b=(1,5); pair c=(0,4); pair d=(1,4); pair e=(4,1); pair f=(5,1); pair g=(4,0); pair h=(5,0); pair y=(0,0); pair s=(5,5);
draw(a--s--h--y--a);
draw(c--d--b,gray);
draw(g--e--f,gray);
draw(d--y--e--s--d);
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f); dot(g); dot(h); dot(y); dot(s);
label("A",a,NW);
label("B",b,N);
label("C",c,W);
label("D",d,SE);
label("E",e,NW);
label("F",f,E);
label("G",g,S);
label("H",h,SE);
label("Y",y,SW);
label("S",s,NE);
[/asy]
Original LaTeX notation
In the figure below, $ABDC,$ $EFHG,$ and $ASHY$ are all squares; $AB=EF =1$ and $AY=5$.

What is the area of quadrilateral $DYES$?

[asy]
size(5cm);
defaultpen(black+1);
pair a=(0,5); pair b=(1,5); pair c=(0,4); pair d=(1,4); pair e=(4,1); pair f=(5,1); pair g=(4,0); pair h=(5,0); pair y=(0,0); pair s=(5,5);
draw(a--s--h--y--a);
draw(c--d--b,gray);
draw(g--e--f,gray);
draw(d--y--e--s--d);
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f); dot(g); dot(h); dot(y); dot(s);
label("$A$",a,NW);
label("$B$",b,N);
label("$C$",c,W);
label("$D$",d,SE);
label("$E$",e,NW);
label("$F$",f,E);
label("$G$",g,S);
label("$H$",h,SE);
label("$Y$",y,SW);
label("$S$",s,NE);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
d38e7610-c626-5224-a23f-e765c933fff2
task_key
geometry--test--d38e7610-c626-5224-a23f-e765c933fff2
task_revision_id
1
config / split
geometry / test

Official source

initial import