Can You Solve this Geometry Puzzle?

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There are 5 semicircles and the three below have a diameter of 4. Can you find the total red area?

This geometry puzzle was asked by Twitter user @Cshearer41. Please give her a follow if you enjoy geometry puzzles.

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Комментарии
Автор

Will definitely be using the phrase "the messes cancel" in future.

elijahjoel
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Interesting how the area is independent of the point taken on the middle semicircle, not an intuitive fact. I also like how you don't go too slow like other youtubers who explain every step, your pace is just perfect. Excellent solution, excellent problem.

enejidjsi
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Very nice, great video!
What I did is I chose a point on the middle semicircle that was also on the line, so I could see the area would be two semi circles with diameters on the line. Since one diameter was two segments of 4 and the other was 1 segment, I knew that one had a diameter of 8 and the other had a diameter of 4. Then I just used the formula for a circle on both added them and divided by 2, (4^2+2^2)PI/2. However this doesn't tell you if the area is the same for any point you choose on the circle, but I just assumed that was true because we were asked to find the area and not a range of areas.

adrienyts
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Keep doing your interesting videos!👍

francisconavarromolina
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Great explanation
i thought the 2 point of 2 semicircle met at the center of the middle semicircle, but it just no matter because the answer will be the same for all point in the middle semicircle

phjvrsh
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I cheated a bit. I chose the point where the middle semicircle intersects the line. In that specific case, it's pretty easy to see that the two semicircles have diameters of 8 and 4, which give a combined area of 10pi. Since you didn't give a specific point on the middle semicircle, I assumed it was true in general.

RunstarHomer
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First one here again, I like that problem BTW








Damn u r so awesome...

HolyG-sus
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I was about to ask where you got the pi over 8 from, but then I realized that you were talking about diameter and not radius! Stupid formulas that get stuck in your head!

oliverhb