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MATH / Two 4×4 squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the ar…

Problem

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

problem

Two 4×44\times 4 squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region created by removing the circle from the squares? [asy] /* AMC8 2004 #25 Problem */ path square=((0,0)--(4,0)--(4,4)--(0,4)--cycle); filldraw(shift(-sqrt(8)/2.0)*rotate(45)*square, lightgrey, black); filldraw(shift(sqrt(8)/2,0)*rotate(45)*square, lightgrey, black); filldraw(circle((0,sqrt(8)), sqrt(8)/2), white, black); [/asy]
Plain-text mathematical notation (without MathML)
Two 4×4 squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region created by removing the circle from the squares? [asy]
/* AMC8 2004 #25 Problem */
path square=((0,0)--(4,0)--(4,4)--(0,4)--cycle);
filldraw(shift(-sqrt(8)/2.0)*rotate(45)*square, lightgrey, black);
filldraw(shift(sqrt(8)/2,0)*rotate(45)*square, lightgrey, black);
filldraw(circle((0,sqrt(8)), sqrt(8)/2), white, black);
[/asy]
Original LaTeX notation
Two $4\times 4$ squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region created by removing the circle from the squares? [asy]
/* AMC8 2004 #25 Problem */
path square=((0,0)--(4,0)--(4,4)--(0,4)--cycle);
filldraw(shift(-sqrt(8)/2.0)*rotate(45)*square, lightgrey, black);
filldraw(shift(sqrt(8)/2,0)*rotate(45)*square, lightgrey, black);
filldraw(circle((0,sqrt(8)), sqrt(8)/2), white, black);
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
1a47399f-3522-5fa4-ad5f-9dac18bb723b
task_key
geometry--test--1a47399f-3522-5fa4-ad5f-9dac18bb723b
task_revision_id
1
config / split
geometry / test

Official source

initial import