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MATH / Three circular arcs of radius 5 units bound the region shown. Arcs AB and AD are quarter-circles, and arc BCD is a semicircle. What is the area, in square units, of the region? [as…

Problem

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problem

Three circular arcs of radius 5 units bound the region shown. Arcs ABAB and ADAD are quarter-circles, and arc BCDBCD is a semicircle. What is the area, in square units, of the region? [asy] /* AMC8 2000 #19 Problem */ draw((0,0)..(1,1)..(2,0)); draw((0,0)..(.7,-.3)..(1,-1)); draw((1,-1)..(1.3, -0.3)..(2,0)); label("AA", (1,-1), SW); label("BB", (0,0), W); label("CC", (1,1),N); label("DD", (2,0),E); [/asy]
Plain-text mathematical notation (without MathML)
Three circular arcs of radius 5 units bound the region shown. Arcs AB and AD are quarter-circles, and arc BCD is a semicircle. What is the area, in square units, of the region? [asy]
/* AMC8 2000 #19 Problem */
draw((0,0)..(1,1)..(2,0));
draw((0,0)..(.7,-.3)..(1,-1));
draw((1,-1)..(1.3, -0.3)..(2,0));
label("A", (1,-1), SW);
label("B", (0,0), W);
label("C", (1,1),N);
label("D", (2,0),E);
[/asy]
Original LaTeX notation
Three circular arcs of radius 5 units bound the region shown. Arcs $AB$ and $AD$ are quarter-circles, and arc $BCD$ is a semicircle. What is the area, in square units, of the region? [asy]
/* AMC8 2000 #19 Problem */
draw((0,0)..(1,1)..(2,0));
draw((0,0)..(.7,-.3)..(1,-1));
draw((1,-1)..(1.3, -0.3)..(2,0));
label("$A$", (1,-1), SW);
label("$B$", (0,0), W);
label("$C$", (1,1),N);
label("$D$", (2,0),E);
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
eeb859d6-8b7d-5e42-b1da-37505dd6e83a
task_key
prealgebra--test--eeb859d6-8b7d-5e42-b1da-37505dd6e83a
task_revision_id
1
config / split
prealgebra / test

Official source

initial import