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

Learn how to find the area of the Green shaded region in a Square. Area of Blue shaded region is 81. Whole circle and quarter circle. Important Geometry and Algebra skills are also explained: Pythagorean Theorem; Area of a circle formula. Step-by-step tutorial by PreMath.com
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Calculate area of the Green shaded region | Area of Blue region is 81 | Important skills explained
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[@sandanadurair5862]

I enjoyed your solution. So nice

[@PreMath]

Excellent! Glad to hear that! Thanks for your continued love and support! You are awesome, Sandanadurai. Keep smiling👍 Love and prayers from the USA! 😀

[@jhill4874]

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

[@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!

[@sail2byzantium]

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.

[@tobiasst6609]

The solution was so unexpected. Great!!!

[@PreMath]

Well said! Thanks for your feedback! Cheers! You are awesome, Tobias. Keep smiling👍 Love and prayers from the USA! 😀

[@philipkudrna5643]

Surprisingly elegant solution!

[@tylerwright6380]

Awesome. Simply awesome!

[@procash1968]

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.

[@jeanmarcbonici9525]

I agree with your figures the square has a side of 23.52 cm. The central angle in the small circle is 138.59° and 55.77° in the quarter circle. But no formula for obtaining these figures is simple.

[@CharlesB147]

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

[@lnofzero]

Another excellent presentation!🎇

[@MrPaulc222]

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

[@VDaniel2006]

Amazing!

[@abdessamadsafri8791]

Thank you, Professor

[@HappyFamilyOnline]

Amazing👍 Thanks for sharing😊😊

[@mohanramachandran4550]

Initially l was confused to solve this sum Your solutions are so simple and interesting Thanks a lot

[@murdock5537]

Great! Many thanks, Sir, this is awesome.

[@ZUBAIR457]

Stunning

[@scooby1282]

I am learning something new everyday thank you so much.

[@Ankitsingh-y4j8m]

Excellent question

[@KAvi_YA666]

Thanks for video.Good luck sir!!!!!!!!!!!

[@PreMath]

So nice of you Thank you! Cheers! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀

[@percussion44]

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

[@batchrocketproject4720]

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!

[@dushyantprajapati7782]

You did it very beautifully

[@Waldlaeufer70]

- 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.

[@PreMath]

Excellent! Thanks for sharing! Cheers! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀

[@mega_mango]

Really interesting one

[@bigm383]

Lovely explanation, thanks Professor!❤

[@shahnwazkhursheed7213]

Amazing sir 😮

[@PreMath]

So nice of you, Shahnawaz Thanks for your continued love and support! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀

[@adiammu4254]

Useful video thank you so much

[@solomou146]

Καλημέρα σας. Πολύ έξυπνη σχολική άσκηση με υποδειγματική λύση

[@nelsonmartins9059]

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

[@santiagoarosam430]

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.

[@vaibhavgupta5359]

Sir this question was beyond my imagination 😅😮

[@pralhadraochavan5179]

Good night sir

[@spiderjump]

let the radius of small circle be r. The radius of quadrant is then 2r. Area of circle = pi•r^ 2 Area of quadrant = pi• 2r•2r/4 = pi•r^2 Hence their areas are equal and therefore the ? Area = 81

[@ashumishra5618]

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

[@PreMath]

Dear Ashu, please send the question to email: [e-mail] Please keep in mind that there are many requests ahead of you. So please be patient. Thanks for asking. Cheers

[@vishwambharmahant9485]

27cm^2each

[@giuseppemalaguti435]

3G+(Ac-81)=1/4(4Ac)...3G=81

[@jaii5955]

I am in 9th and i able to solve it 😲

[@walterdowdle6033]

Premath

[@mohamadtaufik5770]

81 cm2

[@BabitaKumari-gd4mh]

If anyone have dare then find the radius of circle😈 and also for premath

[@marcelowanderleycorreia8876]

Show!!

[@theoyanto]

Brilliant... Never saw this coming, your solutions is magic 🪄