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Geometry 18 Online
OpenStudy (anonymous):

Can someone pleeaase help explain this in the easiest way possible? Thank you (: Find the area of one segment formed by a square with sides of 6" inscribed in a circle. (Hint: use the ratio of 1:1:√2 to find the radius of the circle.)

OpenStudy (anonymous):

you got a picture? not sure what is meant by "one segment formed by a square with sides of 6" inscribed in a circle. "

OpenStudy (anonymous):

|dw:1431831294433:dw|

OpenStudy (anonymous):

No, sadly there is no picture provided. /: @satellite73

OpenStudy (anonymous):

if it is that piece we can do it

OpenStudy (anonymous):

the circle has areas \(\pi r^2\) since the side of the square is 6, the diagonal is \(6\sqrt2\) and so the radius is \(3\sqrt2\)

OpenStudy (anonymous):

the square has areas \(6^2=36\)

OpenStudy (anonymous):

the circle has area \(18\pi\)

OpenStudy (anonymous):

Why the square root of 2? Is that just how it always will be or does that change?

OpenStudy (anonymous):

the length of the diagonal of a square is \(\sqrt2\) times the length of the side

OpenStudy (anonymous):

that was your hint "(Hint: use the ratio of 1:1:√2 to find the radius of the circle.)"

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