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MATH / Quadrilateral ABCD is a square with area 16 square inches. The figure represents the pieces of a Chinese tangram in which all the triangles are isosceles and piece "e'' is a square…

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

problem

Quadrilateral ABCDABCD is a square with area 16 square inches. The figure represents the pieces of a Chinese tangram in which all the triangles are isosceles and piece "e'' is a square. What is the area of the gray piece, in square inches? [asy] fill((2,0)--(4,2)--(4,0)--cycle,gray(.7)); draw((0,0)--(0,4)--(4,4)--(4,0)--cycle,linewidth(1)); draw((0,0)--(4,4),linewidth(1)); draw((1,1)--(2,0)--(4,2),linewidth(1)); draw((0,4)--(3,1)--(3,3),linewidth(1)); label("AA",(0,4),W); label("BB",(4,4),E); label("CC",(4,0),E); label("DD",(0,0),W); label("e",(2,1)); [/asy]
Plain-text mathematical notation (without MathML)
Quadrilateral ABCD is a square with area 16 square inches. The figure represents the pieces of a Chinese tangram in which all the triangles are isosceles and piece "e'' is a square. What is the area of the gray piece, in square inches?

[asy]
fill((2,0)--(4,2)--(4,0)--cycle,gray(.7));
draw((0,0)--(0,4)--(4,4)--(4,0)--cycle,linewidth(1));
draw((0,0)--(4,4),linewidth(1));
draw((1,1)--(2,0)--(4,2),linewidth(1));
draw((0,4)--(3,1)--(3,3),linewidth(1));
label("A",(0,4),W);
label("B",(4,4),E);
label("C",(4,0),E);
label("D",(0,0),W);
label("e",(2,1));

[/asy]
Original LaTeX notation
Quadrilateral $ABCD$ is a square with area 16 square inches. The figure represents the pieces of a Chinese tangram in which all the triangles are isosceles and piece "e'' is a square. What is the area of the gray piece, in square inches?

[asy]
fill((2,0)--(4,2)--(4,0)--cycle,gray(.7));
draw((0,0)--(0,4)--(4,4)--(4,0)--cycle,linewidth(1));
draw((0,0)--(4,4),linewidth(1));
draw((1,1)--(2,0)--(4,2),linewidth(1));
draw((0,4)--(3,1)--(3,3),linewidth(1));
label("$A$",(0,4),W);
label("$B$",(4,4),E);
label("$C$",(4,0),E);
label("$D$",(0,0),W);
label("e",(2,1));

[/asy]

level

Level 3

type

Prealgebra

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Source and history

task_id
059ee619-e73f-59ad-860f-4e7644f7a5da
task_key
prealgebra--test--059ee619-e73f-59ad-860f-4e7644f7a5da
task_revision_id
1
config / split
prealgebra / test

Official source

initial import