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MATH / The two externally tangent circles each have a radius of 1 unit. Each circle is…

Problem

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

problem

The two externally tangent circles each have a radius of 1 unit. Each circle is tangent to three sides of the rectangle. What is the area of the shaded region? Express your answer in terms of π\pi. [asy]import graph; defaultpen(linewidth(.8pt)); fill((-40,20)--(40,20)--(40,-20)--(-40,-20)--cycle,gray); fill(Circle((-20,0),20),white); fill(Circle((20,0),20),white); draw((-40,20)--(40,20)--(40,-20)--(-40,-20)--cycle); draw(Circle((-20,0),20)); draw(Circle((20,0),20)); [/asy]
Plain-text mathematical notation (without MathML)
The two externally tangent circles each have a radius of 1 unit. Each circle is tangent to three sides of the rectangle. What is the area of the shaded region? Express your answer in terms of π.

[asy]import graph;
defaultpen(linewidth(.8pt));
fill((-40,20)--(40,20)--(40,-20)--(-40,-20)--cycle,gray);
fill(Circle((-20,0),20),white);
fill(Circle((20,0),20),white);
draw((-40,20)--(40,20)--(40,-20)--(-40,-20)--cycle);
draw(Circle((-20,0),20));
draw(Circle((20,0),20));

[/asy]
Original LaTeX notation
The two externally tangent circles each have a radius of 1 unit. Each circle is tangent to three sides of the rectangle. What is the area of the shaded region? Express your answer in terms of $\pi$.

[asy]import graph;
defaultpen(linewidth(.8pt));
fill((-40,20)--(40,20)--(40,-20)--(-40,-20)--cycle,gray);
fill(Circle((-20,0),20),white);
fill(Circle((20,0),20),white);
draw((-40,20)--(40,20)--(40,-20)--(-40,-20)--cycle);
draw(Circle((-20,0),20));
draw(Circle((20,0),20));

[/asy]

level

Level 2

type

Geometry

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Source and history

task_id
97a14dd3-9dea-563d-9c54-f8f6c31f2e89
task_key
geometry--test--97a14dd3-9dea-563d-9c54-f8f6c31f2e89
task_revision_id
1
config / split
geometry / test

Official source

initial import