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MATH / A regular octagon ABCDEFGH has an area of one square unit. What is the area of the rectangle ABEF? [asy] pair A,B,C,D,I,F,G,H; A=(-1,1); B=(1,1); H=(-2.41,-0.41); C=(2.41,-0.41); G…

Problem

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

problem

A regular octagon ABCDEFGHABCDEFGH has an area of one square unit. What is the area of the rectangle ABEFABEF? [asy] pair A,B,C,D,I,F,G,H; A=(-1,1); B=(1,1); H=(-2.41,-0.41); C=(2.41,-0.41); G=(-2.41,-2.41); D=(2.41,-2.41); F=(-1,-3.82); I=(1,-3.82); draw(A--B--C--D--I--F--G--H--cycle,linewidth(0.7)); label("AA",A,N); label("BB",B,N); label("CC",C,E); label("DD",D,E); label("EE",I,S); label("FF",F,S); label("GG",G,W); label("HH",H,W); [/asy]
Plain-text mathematical notation (without MathML)
A regular octagon ABCDEFGH has an area of one square unit. What is the area of the rectangle  ABEF?

[asy]
pair A,B,C,D,I,F,G,H;
A=(-1,1);
B=(1,1);
H=(-2.41,-0.41);
C=(2.41,-0.41);
G=(-2.41,-2.41);
D=(2.41,-2.41);
F=(-1,-3.82);
I=(1,-3.82);
draw(A--B--C--D--I--F--G--H--cycle,linewidth(0.7));
label("A",A,N);
label("B",B,N);
label("C",C,E);
label("D",D,E);
label("E",I,S);
label("F",F,S);
label("G",G,W);
label("H",H,W);
[/asy]
Original LaTeX notation
A regular octagon $ABCDEFGH$ has an area of one square unit. What is the area of the rectangle  $ABEF$?

[asy]
pair A,B,C,D,I,F,G,H;
A=(-1,1);
B=(1,1);
H=(-2.41,-0.41);
C=(2.41,-0.41);
G=(-2.41,-2.41);
D=(2.41,-2.41);
F=(-1,-3.82);
I=(1,-3.82);
draw(A--B--C--D--I--F--G--H--cycle,linewidth(0.7));
label("$A$",A,N);
label("$B$",B,N);
label("$C$",C,E);
label("$D$",D,E);
label("$E$",I,S);
label("$F$",F,S);
label("$G$",G,W);
label("$H$",H,W);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
8cb00a58-3602-5da3-8621-a7ba715c404e
task_key
geometry--test--8cb00a58-3602-5da3-8621-a7ba715c404e
task_revision_id
1
config / split
geometry / test

Official source

initial import