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MATH / Two shaded quarter-circles, each with a radius of 4 units, are formed in the 4…

Problem

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

problem

Two shaded quarter-circles, each with a radius of 4 units, are formed in the 4 by 8 rectangular region shown. What is the area of the non-shaded region, in square units? Express the area in the form a−bπa-b\pi where aa and bb are integers. [asy] size(4cm,4cm); pair A,B,C,D,a,b,X; A=(0,0); B=(8,0); C=(8,4); D=(0,4); X=(4,4); draw(A--B--C--D--A); a=(3,1.5); fill((A..a..X--D--A--cycle),gray); draw(A..a..X); b=(5,1.5); fill((B..b..X--C--B--cycle),gray); draw(B..b..X); label("88",midpoint(A--B),S); label("44",midpoint(B--C),E); [/asy]
Plain-text mathematical notation (without MathML)
Two shaded quarter-circles, each with a radius of 4 units, are formed in the 4 by 8 rectangular region shown. What is the area of the non-shaded region, in square units? Express the area in the form a−bπ where a and b are integers.

[asy]

size(4cm,4cm);

pair A,B,C,D,a,b,X;

A=(0,0);
B=(8,0);
C=(8,4);
D=(0,4);

X=(4,4);

draw(A--B--C--D--A);

a=(3,1.5);

fill((A..a..X--D--A--cycle),gray);

draw(A..a..X);

b=(5,1.5);

fill((B..b..X--C--B--cycle),gray);

draw(B..b..X);

label("8",midpoint(A--B),S);
label("4",midpoint(B--C),E);

[/asy]
Original LaTeX notation
Two shaded quarter-circles, each with a radius of 4 units, are formed in the 4 by 8 rectangular region shown. What is the area of the non-shaded region, in square units? Express the area in the form $a-b\pi$ where $a$ and $b$ are integers.

[asy]

size(4cm,4cm);

pair A,B,C,D,a,b,X;

A=(0,0);
B=(8,0);
C=(8,4);
D=(0,4);

X=(4,4);

draw(A--B--C--D--A);

a=(3,1.5);

fill((A..a..X--D--A--cycle),gray);

draw(A..a..X);

b=(5,1.5);

fill((B..b..X--C--B--cycle),gray);

draw(B..b..X);

label("$8$",midpoint(A--B),S);
label("$4$",midpoint(B--C),E);

[/asy]

level

Level 4

type

Prealgebra

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Source and history

task_id
ab1b3237-7272-55eb-96a4-6d337d5197cd
task_key
prealgebra--test--ab1b3237-7272-55eb-96a4-6d337d5197cd
task_revision_id
1
config / split
prealgebra / test

Official source

initial import