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MATH / ABCD is a square with AB=8cm. Arcs BC and CD are semicircles. Express the area of the shaded region, in square centimeters, and in terms of π. (As always, do not include units in y…

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problem

ABCDABCD is a square with AB=8AB = 8cm. Arcs BCBC and CDCD are semicircles. Express the area of the shaded region, in square centimeters, and in terms of π\pi. (As always, do not include units in your submitted answer.) [asy] real y = .866025404; draw((-1,-1)--(1, -1) -- (1, 1) -- (-1, 1)--cycle ); draw( Arc( (1,0), 1, 90, 270)); draw( Arc( (0,1), 1, 180, 360)); fill((0,0)..(.5, y).. (1,1) --cycle, gray(0.7)); fill((0,0)..(y, .5).. (1,1) --cycle, gray(0.7)); label ("AA", (-1,-1) , SW); label ("BB", (1,-1) , SE); label ("CC", (1,1) , NE); label ("DD", (-1,1) , NW); [/asy]
Plain-text mathematical notation (without MathML)
ABCD is a square with AB=8cm. Arcs BC and CD are semicircles. Express the area of the shaded region, in square centimeters, and in terms of π. (As always, do not include units in your submitted answer.) [asy]
real y = .866025404;
draw((-1,-1)--(1, -1) -- (1, 1) -- (-1, 1)--cycle );
draw( Arc( (1,0), 1, 90, 270));
draw( Arc( (0,1), 1, 180, 360));
fill((0,0)..(.5, y).. (1,1) --cycle, gray(0.7)); fill((0,0)..(y, .5).. (1,1) --cycle, gray(0.7));
label ("A", (-1,-1) , SW); label ("B", (1,-1) , SE); label ("C", (1,1) , NE); label ("D", (-1,1) , NW);

[/asy]
Original LaTeX notation
$ABCD$ is a square with $AB = 8$cm. Arcs $BC$ and $CD$ are semicircles. Express the area of the shaded region, in square centimeters, and in terms of $\pi$. (As always, do not include units in your submitted answer.) [asy]
real y = .866025404;
draw((-1,-1)--(1, -1) -- (1, 1) -- (-1, 1)--cycle );
draw( Arc( (1,0), 1, 90, 270));
draw( Arc( (0,1), 1, 180, 360));
fill((0,0)..(.5, y).. (1,1) --cycle, gray(0.7)); fill((0,0)..(y, .5).. (1,1) --cycle, gray(0.7));
label ("$A$", (-1,-1) , SW); label ("$B$", (1,-1) , SE); label ("$C$", (1,1) , NE); label ("$D$", (-1,1) , NW);

[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
7711248e-f390-5c93-9818-113e5a519493
task_key
geometry--test--7711248e-f390-5c93-9818-113e5a519493
task_revision_id
1
config / split
geometry / test

Official source

initial import