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MATH / ABCD is a square 4 inches on a side, and each of the inside squares is formed by joining the midpoints of the outer square's sides. What is the area of the shaded region in square …

Problem

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

problem

ABCDABCD is a square 4 inches on a side, and each of the inside squares is formed by joining the midpoints of the outer square's sides. What is the area of the shaded region in square inches? [asy] draw( (-1,-1)--(1,-1) -- (1,1) -- (-1,1)--cycle); draw( (-2,-2)--(2,-2) -- (2,2) -- (-2,2)--cycle); draw( (-2, -2) -- (2, -2) -- (2,2) -- (-2 ,2)-- cycle); draw( (0, 2) -- (2,0) -- (0, -2) -- (-2, 0)-- cycle); draw( (0, 2) -- (2, 0) -- (0 , -2) -- (-2 ,0)-- cycle); filldraw( (-1, -1) -- (1, -1) -- (0, -2)--cycle, gray); filldraw( (1, -1) -- (1, 1) -- (2, 0)--cycle, gray); filldraw( (1, 1) -- (-1, 1) -- (0, 2)--cycle, gray); filldraw( (-1, 1) -- (-1, -1) -- (-2, 0)--cycle, gray); label("AA", (-2,2), NW); label( "BB", (2,2), NE); label( "CC", (2,-2), SE); label( "DD", (-2,-2), SW); [/asy]
Plain-text mathematical notation (without MathML)
ABCD is a square 4 inches on a side, and each of the inside squares is formed by joining the midpoints of the outer square's sides. What is the area of the shaded region in square inches?

[asy]
draw( (-1,-1)--(1,-1) -- (1,1) -- (-1,1)--cycle); draw( (-2,-2)--(2,-2) -- (2,2) -- (-2,2)--cycle);
draw( (-2, -2) -- (2, -2) -- (2,2) -- (-2 ,2)-- cycle); draw( (0, 2) -- (2,0) -- (0, -2) -- (-2, 0)-- cycle);
draw( (0, 2) -- (2, 0) -- (0 , -2) -- (-2 ,0)-- cycle);

filldraw( (-1, -1) -- (1, -1) -- (0, -2)--cycle, gray);
filldraw( (1, -1) -- (1, 1) -- (2, 0)--cycle, gray);
filldraw( (1, 1) -- (-1, 1) -- (0, 2)--cycle, gray);
filldraw( (-1, 1) -- (-1, -1) -- (-2, 0)--cycle, gray);

label("A", (-2,2), NW);
label( "B", (2,2), NE);
label( "C", (2,-2), SE);
label( "D", (-2,-2), SW);

[/asy]
Original LaTeX notation
$ABCD$ is a square 4 inches on a side, and each of the inside squares is formed by joining the midpoints of the outer square's sides. What is the area of the shaded region in square inches?

[asy]
draw( (-1,-1)--(1,-1) -- (1,1) -- (-1,1)--cycle); draw( (-2,-2)--(2,-2) -- (2,2) -- (-2,2)--cycle);
draw( (-2, -2) -- (2, -2) -- (2,2) -- (-2 ,2)-- cycle); draw( (0, 2) -- (2,0) -- (0, -2) -- (-2, 0)-- cycle);
draw( (0, 2) -- (2, 0) -- (0 , -2) -- (-2 ,0)-- cycle);

filldraw( (-1, -1) -- (1, -1) -- (0, -2)--cycle, gray);
filldraw( (1, -1) -- (1, 1) -- (2, 0)--cycle, gray);
filldraw( (1, 1) -- (-1, 1) -- (0, 2)--cycle, gray);
filldraw( (-1, 1) -- (-1, -1) -- (-2, 0)--cycle, gray);

label("$A$", (-2,2), NW);
label( "$B$", (2,2), NE);
label( "$C$", (2,-2), SE);
label( "$D$", (-2,-2), SW);

[/asy]

level

Level 2

type

Geometry

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Source and history

task_id
a469894c-ef10-5222-8152-07a6df273182
task_key
geometry--test--a469894c-ef10-5222-8152-07a6df273182
task_revision_id
1
config / split
geometry / test

Official source

initial import