Find the Area of the Blue Shaded Region | Step-by-Step Tutorial

[sangam]

Amazing sir😍😍😍 ... thnxx for this video ... and yaah i m proud to do 1st comment on ur video ... 😎😎

[Msmaxine]

This was the best demonstration for me. I've watched other videos but they were difficult to understand. Thank you for clearing this up and making it much simpler to understand!

[nakamakai]

Beautiful work and explanation - I hope lots of people are learning a lot from your tutorials, well done. More like this, please!!

[thomaskeating]

The beauty is both your patience as well as highlighting the insights that conquer the problem. You must, in your mind, arrive to the solution so quickly, but you allow the audience to see it step by step. Maybe you could speed up the trivial steps and explain some of the (non obvious) clues that really break the problems wide open. Regardless, great work.

[ابوفراس-قد]

Thank you, Mr. I really enjoy the issues that you raise and solve in a simple and useful way. 👍

[shashidharn]

Not mentioned in the question that curve is forming quarter of circle, unless you give curve radius you can't find the area

[HappyFamilyOnline]

Great video sir 👍
Thank you so much for sharing this amazing video🎉

[riotangel]

Great video. But I have another solution :
Blue shaded area = area of 2 1/4 circle - area of the square
= 2. 1/4 πr^(2) - s^(2)
= 1/2. 3, 14. 2^(2) - 2^(2)
= 1/2. 3, 14. 4 - 4
= 6, 28 - 4
= 2, 28

[williamwingo]

The area of each unshaded region is the area of the square minus the area of the quarter-circle;
or (2 squared) - ((pi)(2 squared)/4);
which equals 4 - (4 pi/4) = 4 - pi.
There are two identical unshaded regions, so the area of the shaded region is the area of the square minus twice that figure;
or 4 - ((2)(4 - pi));
which equals 4 - (8 - 2 pi) = -4 + 2 pi = 2 pi - 4.
Thank you, ladies and gentlemen; I'll be here all week.

[devondevon]

Answer 2.2857
The area of the circle is 22/7 x 4 = 88/7 but since it is a quarter of a circle then 88/7 x 1/4 = 88/28 =3.1428 (or pie).
Since the area of square = 4, then the area of the triangle that bisects the shaded region is 2, then half the area of the shaded region is 3.1428- 2 =1.1428, then the entire shaded region is 1.1428 x 2 or 2.2857.
A nice one.

[MrSudhir]

Good problem and solution. I was thinking of two tangents of a circle meeting at right angles and so forth.

[hwxpaisho]

Thank you so much it will help me a lot.

[xof-woodworkinghobbyist]

Great solution.
I did it a bit differently (with the same end result!):
Area of the square: s^2 = 2^2 = 4
Area of a quadrant of circle: Pi r^2/4 = Pi
Area of one white zone: Area of square - Area of quadrant = 4 - Pi
There are 2 white zones: 2 x (4 - Pi) = 8 - 2Pi
Blue area = Area of square - area of 2 white zones = 4 - (8 - 2Pi) = 2Pi -4 = 2.28 (Pi = 3.14)

[timreed]

(Area of Half Circle) - (Area of Square) is easier.
((pi * 2^2)/2) - 2^2 = 2.28

[jesusmeghrajani]

Hi! I love this video 💚 May I ask for your kind help? I tried using the formula for the area of the sector and the segment of the circlr to get the area of the blue region. It is quite confusing to me not to get the 1/4 of the area of the circle using the area of a sector formula. May I ask for some insights please, if possible? Take care and thank you for giving us great problems to work at. God bless

[modasudheendra]

Sir please let us know the software and tools you are using to make this presentation video and recording. Thank you

[rmatalanga]

How did you conclude that the area formed by the triangle and the chord is a quarter is a circle?

[TurquoizeGoldscraper]

I took the two quarter circles, each consists of the blue region and one of the white regions, so both added together give you two white regions and two blue regions. The square consists of both white regions and the blue region. If you add the two quarter circles and subtract the square, you get the blue region.

[xalkxalk]

Little bit different... 1/4 of circle πr²/4 . Area rectangle 2². One white area y=2²-πr²/4=4-π . Two white area 2*(4-π)=8-2π. Blue area=Rectangle-2 White area . Blue A=4 - (8-2π)=4 - 8 + 2π= 2π-4 = 2* (π - 2)!

[ezioauditore]

I multiplied the area of ​​the circular sector by two and subtracted the area of ​​the square from this.