Calculate area of the Green shaded region | Area of Blue region is 81 | Important skills explained

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Calculate area of the Green shaded region | Area of Blue region is 81 | Important skills explained

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[jhill]

Yet another sneaky, yet completely legitimate, solution. Thanks!

[sailbyzantium]

That's very clever. I confess I was stumped but the solution as based on the areas of the full circle and the larger quarter circle being equivalent was a bit of an unexpected mind-blower, but the logic of it is readily apparent in how you solved it.

[JLvatron]

What a clean solution!
Initially I figured the blue arc (the only numerical information given) would be required to calculate the radius.
Then I did the equation, and discovered the observation.
Very good!

[tobiasst]

The solution was so unexpected. Great!!!

[procash]

Super Premath Guru Ji

A good problem for my son to solve this weekend. Will show him the video tomorrow evening. Thanks

[waheisel]

Thank you PreMath for another great math puzzle 😊. An even more challenging problem is to find the radius of the circle.
I brute forced my way to that. I setup a Cartesian coordinate and used algebra to find the intersections of the circle and the quarter circle. Then used the arc tangent function on a calculator to get the central angle of the arc to be 138 degrees, and the same angle for the quarter circle to be 55°. Then I did some serious algebra and geometry to get the radius of the small circle to be 11.76 cm. I'm guessing one of you-all has a better / more elegant solution than that.

[CharlesB]

That was very elegantly done. Reminds me of Hippocrates' lune problems.

[MrPaulc]

Good stuff! I couldn't figure out how to get started on this. I went down a couple of blind alleys then gave up.

[scooby]

I am learning something new everyday thank you so much.

[percussion]

Pretty neat. nary a calculation, just a lot of observation and discovery of what equals what.

[nelsonmartins]

It would be nice if you could, show us which strategy you willl bem using to find the solution, before start solving the problem.

[Waldlaeufer]

- The radius of the green quarter circle is twice the radius of the blue small circle.
- Therefore, the complete green circle has four times the area of the blue circle.
- So, the green quarter circle must have the same area as the blue circle.
- The blue circle and the green quarter circle share the white area inside each of them.
- Finally, the blue area (81 cm²) of the blue circle must be the same area as the green area of the quarter circle.
The green area, therefore, is 81 cm².

[mohanramachandran]

Initially l was confused to solve this sum

Your solutions are so simple and interesting
Thanks a lot

[murdock]

Great! Many thanks, Sir, this is
awesome.

[batchrocketproject]

I'm glad I tackled this before watching the video. It is a wonderful problem. Really enjoyed the video steps - especially formalising the final equivalence into an equation and solving xyz (the part I did in my head). Thanks!

[solomou]

Καλημέρα σας. Πολύ έξυπνη σχολική άσκηση με υποδειγματική λύση

[bigm]

Lovely explanation, thanks Professor!❤

[misterenter-izrz]

Also a terrific design of puzzle, blue region and green regions are of the same area, so answer is just 81.🤩

[santiagoarosam]

Lado del cuadrado =R 》Zona verde =(Cuadrante círculo radio R) - (Zona blanca círculo radio R/2) =[Pi(R^2)/4] - [Pi(R^2/4)-81] =81
Gracias y un saludo.

[ashumishra]

Sir, I've a doubt that (1= -1) Proof: (1)²=1
and (-1)²=1 R.H.S are equal of both the equations then L.H.S will have to equal (1)²=(-1)²=> 1=-1 [because mª=nª=> m=n]
Sir how is it possible ( 1=-1 ).
Please make a video about this topic.
Sir I humble request of you