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Circles and Square

Directions: The diagram shows a square and four semicircles formed using each side of the square as a diameter. What fraction of the square is shaded?



How can you partition the space to find the area you need?



(Π-2)/2  (Thanks to Tracy Parry for correcting the answer)

Source: Dylan Kane

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  1. I’m stumped, can someone shed some light on where to start and where to partition?

    • Divide it into fourths and find the space between the smaller square and the quarter of a circle. Once partitioned you can see that there are eight of these empty spaces which comprise the non-shaded space.

  2. My grade 8 students and I still don’t fully understand the answer that is given. Is there anyone who might be able to show us how they got to this answer?

    Thank you!!

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