SOLUTION: a square is inscribed in a circle. if the diagonal of the square measures 6 in. what is the exact area of the circle?
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Question 328504: a square is inscribed in a circle. if the diagonal of the square measures 6 in. what is the exact area of the circle?
Found 2 solutions by galactus, solver91311:
Answer by galactus(183) (Show Source): You can put this solution on YOUR website!
Let a circle side be x.
Since the sides are all the same length, we have
Since this is a side length, the circle's radius is half that.
The area of a circle is with
area of circle:
As an added bonus, the area of the square is 18.
the ratio of the square area to the circle area is
This is true in general.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If a square is inscribed in a circle, then the diagonal of the square is a diameter of the circle. Half of the diameter is the radius. Square the radius and multiply times 
. Leave it in terms of for the exact answer.
John
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