Area Problem #15


A square is inscribed in a white circle as shown. Semi-circles are then drawn onto each side of the square.

If the white arc AB = 5cm, find the total area of the orange shapes.

23 thoughts on “Area Problem #15

  1. That’s the third time I’ve meddled after posting. First time was because someone pointed out it was geometrically impossible. Second and third time were both less than 5 mins after posting, but you’d already started them both!! Apologies.

  2. This provided great practice on many key skills, namely written mathematical communication, for one of my top set Y11’s. I then extended for those that finished by asking to find in terms of Pi. Brilliantly accessible yet effective question, thank you!!

    • I’ve calculated the area of the epicycloid, and I think (hope :)) that’s right (5.9683), and after the area of the square using Pitagora to find the length of one side (note that I’m not studying math so I’m solving this with my current skills).. Can you tell me where I’m making errors? (p.s. Don’t tell me the result if you can :))

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