Thanks for bringing my memory of the Sector Area back
@vidyadharjoshi5714
Жыл бұрын
ht of triangle ABC = sqrt(16-4). Area ABC = 0.5*4*3.46 = 6.93. Green Area = = Area of triangle ABC - 3*60 deg part of circle. = 6.93 - 2pi = 0.645
@PreMath
Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@AnonimityAssured
Жыл бұрын
I think I can see a very simple way of doing this. Spoiler alert. The green area will be the area of an equilateral triangle of side-length 4 minus the area of a semicircle of diameter 4. Area of triangle = 4√3. Area of semicircle = 2π. Green area = 4√3 − 2π = 2(2√3 − π) square units. Numerical equivalent ≈ 0.645 square units.
@bobeyay
Жыл бұрын
I've been watching your content for some while now and finally for the first time in a long time, I manage to solve one! Thanks for making my interest in Math come back again, it was one of my favorite subjects back in my days in school
@muttleycrew
Жыл бұрын
Enjoyed solving this one. Solving these geometric problems is especially satisfying for whatever reason.
@PreMath
Жыл бұрын
Excellent! Glad to hear that! Thanks for your feedback! Cheers! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀
@User-jr7vf
Жыл бұрын
yep,it makes you feel smart
@muttleycrew
Жыл бұрын
@@User-jr7vf That doesn't really explain why solving the geometric problems is more satisfying that solving arithmetic or algebraic problems. It's a personal preference for geometry I'm talking about. I think it's related to the what you see is what you get nature of geometry. There's something immediate about its transparency.
@User-jr7vf
Жыл бұрын
@@muttleycrew I got it
@batavuskoga
Жыл бұрын
My first thought was drawing a square around the circles for calculating. Then I saw I realised it wasn't possible to find the solution this way. Suddenly I saw it. I've drawn a triangle like in the video and find the solution as shown in the video. And of course I found the solution myself and then I checked if I've done it the right way.
@mraymanhassan
Жыл бұрын
Excellent thanks
@eamonhannon1103
Жыл бұрын
Well done !! Clearly presented !
@Copernicusfreud
Жыл бұрын
Yay! I solved it.
@PreMath
Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@lindafromcalifornia1155
Жыл бұрын
That was so beautifully explained. Splendid job Pre-Math.
@alexrocha9191
Жыл бұрын
Good Morning MASTER Thanks Sir A Hug from Rio de Janeiro
@PreMath
Жыл бұрын
So nice of you, Alex Thanks for your continued love and support! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀
@misterenter-iz7rz
Жыл бұрын
The answer is the difference of area of the triangle and the semicircle=(4x4 root 3/2)/2-pix2^2=0.645 approximately.
@PreMath
Жыл бұрын
Great! Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@HappyFamilyOnline
Жыл бұрын
Awesome👍 Thank you so much for sharing.😊
@PreMath
Жыл бұрын
Thanks for your continued love and support! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀
@erautome
Жыл бұрын
1)calculer la hauteur du triangle avec Pythagore. 2) calculer la surface d'un cercle. 3) calculer la surface du morceau d'un cercle inclus dans le triangle. Le triangle étant équilatéral, les angles sont de 60° ou 1/6 de l'aire du cercle. On multiplie l'aire des trois quartier de cercle par 3 et on soustrait de l'aire du triangle.
@jan-willemreens9010
7 ай бұрын
... Good day, Coincidentally I derived the general formula of the area in between 3 identical circles with radius R (lol) ... so Area = [ SQRT(3) - pi/2 ] * R^2 ... finally applying to your problem, where R = 2 ... A(Green shaded region) = 4*SQRT(3) - 2*pi ... thanks for your presentation .... best regards, Jan-W
@KAvi_YA666
Жыл бұрын
Thanks for video.Good luck sir!!!!!!!!!!!!!
@PreMath
Жыл бұрын
Thanks for your continued love and support! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀
@nilsalmgren4492
Жыл бұрын
That one is easy to see how it is done. I figured it out in about 30 seconds, including the sectors of the three circles making half a circle.
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@bentels5340
Жыл бұрын
Solved it the same way (without expounding on the height of the triangle, obviously 😅).
@PreMath
Жыл бұрын
Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@williamwingo4740
Жыл бұрын
No peeking: Consider triangle ABC. Invoking Pythagoras, altitude = 2 sqrt(3); base = 4; and area = (1/2)(2)(sqrt(3))(4) = 4 sqrt(3). The three 60-degree circle segments inside the triangle add up to 180 degrees, which is half the area of one of the circles, or (1/2)(4)(pi) = 2 pi. The green shaded area is the difference, or 4 sqrt(3) -- 2 pi. Staying sharp, one problem at a time.... 🤠
@PreMath
Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@williamwingo4740
Жыл бұрын
@@PreMath Thanks. As I may have said before, the USA needs all the love and prayers it can get.
@mherghulinyan2074
Жыл бұрын
2*sqrt(3)*radius - pi/2*radius^2 ~ 0.645
@PreMath
Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@MrPaulc222
Жыл бұрын
Without a calculator or putting pen to paper I calculated the area of the equilateral and the 1/6th circles and ended up with 4root3 - 2pi. The calculator gives that as 0.645(3dp) sq units. I'm fairly ancient and trying these puzzles helps keep my mind alert and active.
@sorourhashemi3249
3 ай бұрын
Thanks. I got 0.648 square units. For getting area I used Heroin formula= rad.48
@rudychan8792
Жыл бұрын
Angles Are the Same. No Need Phytagoras there, Pal. 😓 Area = (1/2)•4•4•sin60° =4√3 Sectors = 3×(60°/360°)×π×2" = 2π Green = 4√3 - 2π = 0.645 units" Anyway, I give U #161st thumb's Up 🙂 👍
@PreMath
Жыл бұрын
Many approaches are possible to find the solution to this problem! Glad to see the Trigonometry! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@wackojacko3962
Жыл бұрын
The approximation is what's killing me here! Because I like exact! So I'm thinking because Pi and 3^⅓ are so Fractal so too speak... I don't know, just throw the resulting 0.645 square units out the curved space window. I'm just trying too be funny...I absolutely love your channel.
@PreMath
Жыл бұрын
Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@geraldillo
Жыл бұрын
It doesn't make sense to me write the outcome as a decimal fraction. pi is just pi and you can't add it with any other number to get a nice result. I would write it like this; green area= 2(2√3-π)
@piersonm5574
Жыл бұрын
Haven't seen it yet, my guess is you construct an equilateral triangle ABC, then subtract the area of the three segments? The angle is 60°, convert into radians and get the three areas, subtract from ABC's area
@DaftdogUK
Жыл бұрын
Is there a reason we end up approximating to the numerc value? When I did math(s) at school we were taught that unless the question specifically asked for a decimal representation we had to leave the problem with its actual exact value. So our answer would be 4(sq.root3)-2pi. If we converted that to a decimal we would be marked down. It wouldn't be wrong as such, just not properly right. It is however over 40 years since I sat at a school desk. Note - any of our tech/science courses would expect a decimal, but math(s) was a 'pure' subject, not subject to the vagaries of spherical cows in a vacuum.
@User-jr7vf
Жыл бұрын
I also find it odd that he is always approximating his otherwise exact answers.
@joedavis6522
Жыл бұрын
He does derive the exact solution first. I was taught to estimate the answer first, so that I could evaluate the reasonableness of my answer. The green area looked to me to be about a tenth the area of one of the circles. The area of each circle is about 12. So I guess the answer should be about 1. His answer was within a factor of 2 of my guess, so my comfort level would be reasonably high. There is no way I could see this by looking at the exact solution.
@steve1978ger
Жыл бұрын
I find that reducing it to single number can be helpful for a "reality check" of the result. So probably, I'd give both, the exact and the numeric.
@geraldillo
Жыл бұрын
I didn't know the sector area formula and to be honest I don't really understand why it works. But since we deal with an equilateral triangle each angle is 60 degrees and therefore each sector area is one sixth of a circle. So 3 times the area of a circle divided by 6 =3/6 the area of a circle =(r^2*π)/2 green region =area of trianle minus (area of circle divided by 2) =2√3-(r^2*π)/2 (r=2) =2√3-4π/2 =2√3-2π =2(2√3-π)
@albertofernandez6861
Жыл бұрын
La solución es 4√3-2π mediante cálculo mental.
@philipkudrna5643
Жыл бұрын
Before watching: equilateral triangle with sidelength 4 (2r) has the area 4/2*2*sqrt(3) (1/2*base*height) or 4*sqrt(3). From that we deduct 3 circle segments of 60 degrees each or the area of half a circle with the radius 2 or 1/2*4*pi or 2*pi. Thus, the solution is 4*sqrt(3)-2pi or 2(2Sqrt(3)-pi).
@theoyanto
Жыл бұрын
Nice... I like these, thanks again 👍🏻
@joserobertooliveira2082
Жыл бұрын
Belo exercício muito bom
@AmirgabYT2185
7 ай бұрын
S=4√3-2π≈0,64
@florh
Ай бұрын
not seen it yet but the square root of 3 minus pi over 2? Isn't that how to calculate the area between 3 mutually tangent unit circles?
@krishnaramachandran7722
Жыл бұрын
area of an equilateral triangle is sqrt 3/4* a^2.
@gelbkehlchen
Жыл бұрын
Solution: The middlepoints of the 3 circles form a triangele with 3 equal sides of s = 2+2 = 4. The area of this triangle is: s*s/2*√3/2 = s²*√3/4 = 4²*√3/4 = 4*√3. The area of the 3 circle sections with the angle of 60° is together the area of a semicircle. And the area of the green shaded region is: 4*√3-π*2²/2 = 4*√3-π*2 ≈ 0.6450
@eckhardfriauf
Жыл бұрын
For lack of time: 1 equilateral triangle CBA, length of each side = 2*2. then 3 sectors, 60° each --> Area corresponds to π*r²/2 .... etcetera. Please forgive the hurry.
@PreMath
Жыл бұрын
Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@ybodoN
Жыл бұрын
As a formula: the green area is r² (√3 - π/2) where r is the radius of the circles.
@bigm383
Жыл бұрын
Thanks Professor. Another great problem.❤🥂
@PreMath
Жыл бұрын
Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@santiagoarosam430
Жыл бұрын
Los centros de los círculos de radio r=2, tangentes entre sí, corresponden a los vértices de un triángulo equilátero de lado 2r=4 → Área zona verde = (Superficie del triángulo equilátero) - (Superficie de tres sectores circulares de r=2 y ángulo de 60º) = [(4x4√3/2)/2] - [π2²(3x60/360)] =(4√3) - (2π) =0.6450 Gracias y un saludo cordial.
@PreMath
Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@steve1978ger
Жыл бұрын
Well, I screwed it up. I tried to calculate the outer triangle with Pythagoras, but didn't pay attention to what was the hypotenuse. Haven't been doing this a lot since my school days... never too late to (re-)learn things!
@ravipratapsingh4411
Жыл бұрын
Hi sir
@PreMath
Жыл бұрын
Hello dear Thank you! Cheers! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀
@JV-sk5rl
Жыл бұрын
A=((√3)-π/2)r^2
@piccalillipit9211
Жыл бұрын
*0.645* [no units] but Im not ashamed to admit it - my covid riddled brain took 3 failed attempts before I got it
@user-bc4ji6rd6p
Жыл бұрын
これは簡単すぎた。
@PreMath
Жыл бұрын
良い ありがとう
@rikschaaf
Жыл бұрын
Ok, now solve it using the area of a hexagon, rather than a triangle.
@davidcolver2502
Жыл бұрын
These videos are slow even when playback speed is set to 200%.
Пікірлер: 74