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.

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Is A the midpoint of the arc? Ie equidistant from b and the bottom left corner?

I’m about to change it, I’ve had a better idea.

But I’m halfway through solving it!

lol. You can keep that one. Yes, it was intended to be perpendicular to square midpoint. This new version is smarter.

Where’s version 2? And was i right to assume you meant it was 4cm from a to b in a straight line, or did you mean along the arc?

i meant straight line. You’re highlighting all the reasons I’ve rewritten it. There were too many assumptions to be made in the original version. V2 is already up. V1 was only there for a few minutes.

You should get 64 for the original one.

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.

Haha, no worries. Thanks for providing great stimulus!

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!!

Great to hear. Many do these puzzles but the original intention was to challenge school students. I’m pleased you find them a useful resource. ðŸ™‚

134,31..?

Edit:100.52

noop ðŸ™‚

16.1004185???

nope. If you can spot that the orange square is equal in area to the other orange bits it’s a lot easier.

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 :))

50?

Noop I think the answer is already in the comments

ahh.. yeah. I randomly forgot a pi half way through.

400/pi^2

Nice area problem

good job ðŸ™‚

â‰ˆ 40.5 cm^2