How to Find the Percentage of Area Outside a Square Inscribed in a Semicircle?

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To find the percentage of the area outside a square inscribed in a semicircle, one must first calculate the area of both the semicircle and the square. Drawing lines from the center of the semicircle to the square's vertices can help visualize the relationship between the two shapes. The area of the semicircle can be determined using the formula A = (1/2)πr², while the area of the square is calculated based on its side length. After finding both areas, the percentage of the area outside the square can be determined by subtracting the square's area from the semicircle's area and then dividing by the semicircle's area. This approach will lead to the solution of the problem.
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Homework Statement



A square of maximum area is inscribed in a semicircle as shown. What percent (rounded to the nearest tenth) of the area of the circle is outside the square?

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Homework Equations





The Attempt at a Solution



I'm so desperately lost, someone, please help me! :'(

It would be greatly appreciated if you could!
 
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Hint: draw some dotted lines from the center of the circle to the points where the square meets the circle.

Once you do that, you will probably be able to figure out what to do. If you can't, work on it for a bit and then tell us what you've tried and we'll have more help for you.
 

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