Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
I'm not exactly sure what this is asking.....if it is asking for the area between one side of the square and the perimeter of the circle, we can proceed as follows :
To find the radius of the circle we have that
2r^2 = 36 divide both sides by 2
r^2 = 18
r = √18
So....the area we are looking for is the area of a quarter circle with a radius of √18 minus the area of an isosceles right triangle with legs of √18 and a hypotenuse of 6
So....the area is
pi (r^2) /4 - (1/2) (product of leg lengths) =
pi (√18)^2 / 4 - (1/2)(√18)(√18) =
18 ( pi /4 - 1/2) units^2
