express answer in exact form.

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.)

4.5 pi in.^2 - 9 in.^2

Step-by-step explanation:

First, bisect the chord (one side of the square) in half. Draw a line from the middle of the chord to the center of the circle. This will bisect the 90o (o = degree sign) central angle in half, creating a 45o angle.  

So, you have a 45-45-90 triangle. Use the rules for 45-45-90 triangles to determine that the hypotenuse is 3 sqrt 2.  

The hypotenuse of the triangle is the radius of the circle. So now you can find out the area of the circle: A = pi * r^2 --> A = 18 pi in.^2.  

From this information, you can figure out the area of the sector. Do 90o (since the sector angle is 90o) divided by 360o: 90/360. You should get 1/4 (this shows that the sector is a quarter of the square). Next, do 1/4 times the area of the circle --> 1/4 * 18 pi = 4.5 pi in.^2.  

Finally, find out the area of the triangle by using the formula for the area of triangles: A = 1/2 * b * h ---> A = 1/2 * 6 * 3 (we know the base and height from earlier calculations with the 45-45-90 triangle). So --> A = 9 in.^2.  

Lastly, to find the area of one segment, do the area of the sector - the area of the triangle: 4.5 pi in.^2 - 9 in.^2 (This is in exact form. The approximate form would be 5.14 in.^2).

Hope this helps! :)

after simplifying it i got: -36.25 as my answer. hope that !

51-50

step-by-step explanation: