SOLUTION: I need to find the area of a shaded region in which a rectangle is inside a circle. The shaded region is between the rectangle and the circle. I have been given two plots: (3,4)

Question 181908This question is from textbook Discovering Geometry
: I need to find the area of a shaded region in which a rectangle is inside a circle. The shaded region is between the rectangle and the circle. I have been given two plots: (3,4) and (5,0). Please help This question is from textbook Discovering Geometry

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I need to find the area of a shaded region in which a rectangle is inside a circle.
The shaded region is between the rectangle and the circle.
I have been given two plots: (3,4) and (5,0).
:
Assuming that the circle center is at origin (0,0), look at a diagram it will
be apparent that the radius = 5
:
find the area of the circle
A = pi*5^2
A = 78.54 sq units
:
the coordinates of the rectangle given as 3,4 and 5.0, therefore
the other two coordinates will be -3,-4 and -5,0
:
Find the dist between 3,4 and 5,0 for one side of the rectangle
d =
d =
d =
d =
d = 4.47 units is one side
:
Find the dist between 3,4 and -5,0 for the other side of the rectangle
d =
d =
d =
d =
d = 8.94 units is other side
:
Rectangle area: 4.47 * 8.94 = 39.98 sq unit
:
Shaded area = 78.54 - 39.98 = 38.56 sq unit is shaded
:
:
We can also see the diameter (10 units) is = to the diagonal of the rectangle:
Use this fact to check our rectangle dimensions:
on a calc, enter: = 9.995 ~ 10, close enough

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