A square with sides 12 is overlapped by a circle, what is the area of the shaded region?

How to find the area of a region - overlapping square and circle.
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[@kevinwilson960]

Hey John. I’m in my fifties and I’m just a high school graduate. Math was my second worst subject in school. I just couldn’t get it. Over my working career I realized how much math is important. I then realized I had to get better at it. I developed some skills on my own. I have a job that requires me to understand how to come up with the correct answers, using math. I love to watch your channel. You explain how to use math in a very practical way that is easy to understand. I get a lot out of your videos that I wish I knew many years ago. Thank you.

[@tomtke7351]

area of square (12^2) - area of half circle (1/2)(pi×r^2) = 18pi 144 - 18pi = 18(8 - pi) units^2 = 18(4.8584) = 86.45 units^2

[@mikeorgan1993]

No criticism but in the UK we always go to at least 3 decimal places for pi this minimizes the rounding error. As an engineer I preferred 5 decimal places for tolerances of 1/100th of a mm or one thou.

[@derrickbonsell]

Area of circle: pi*r² Area of square: s² Need to take half the area of the circle and subtract it from the square. Side length of square is 12 and the radius of the circle is half of that so 6. Using 3.14 as an approximation of pi. Area=s² - ((2pir²)/2) Area=12² - ((2pi(6)²)/2) Area=144 - ((2pi36)/2) Area=144 - (113.04/2) Area=144 - 56.52 Area=87.48 The shaded area of these two shapes combined is approximately 87.48 units. Edit: forgot that the unit is squared

[@dlkline27]

I got 87.45 but I used 3.1416 for pi which may explain the difference. Love these opportunities for some mental gymnastics.

[@rattywoof5259]

Used 355/113 - very good approximation of pi.

[@johnnyllooddte3415]

area of the square - minus 1/2 the area of the circle

[@betqpublic9901]

For kids I work with some would get stuck on the square not being identified as a given from the beginning.

[@russelllomando8460]

woo hoo...got it. thanks for the fun.

[@deograciousuwiragiye8429]

87.5 for shaded part.

[@TheFallibleFiend]

Let A = the shaded area = the area of the square minus the half the area of the circle. Then A = 12² - ½π(6²)= 144 - 18π This is exactly the kind of problem with which algebra students should be practicing and more advanced students should be refreshing themselves.

[@billbrewster4438]

87.45

[@kennethwright870]

144-18pi

[@beatsinabar]

144-π18

[@kmccray7933]

87.4

[@llywyllngryffyn8053]

87.45 units^2.

[@truxton1000]

15 minutes video on explaining this?? I could explain it to anyone in 30 seconds, is this because it's an American guy doing it, loving the sound of his voice??

[@harrymatabal8448]

Very tru😂

[@ndailorw5079]

…be honest… if you knew nothing about this stuff as you now do, do you think you could Thoroughly grasp and understand the ideas and concepts behind it all? Like… why square, and squared units; and why cube, and cubed units; why A = pi•r^2, A = 1/2 lw, etc. Not knowing those things and other things crucial and necessary to doing math would you really and truly be able to understand problem in 30 seconds? This guy aims is more particularly aimed at those who aren’t quite as “bright” as you are…? And if you can teach “anyone” to do this problem in 30 seconds I’m willing to bet that you will teach nothing of the concepts fundamental and foundational to understanding how to do the problem in 30 seconds, actually. Doing the math is easy, relatively speaking; understanding the concepts beneath and behind it all and deciding upon that knowledge which math to use and how best and most efficient to do se it is quite another thing all together. If this is below your level then move up to something higher and newer and more demanding to you. This is for the uninitiated and even the rusty. I agree he’d do well and do more in less time if he’d streamline his method and approach more. But this is, after all, a program geared toward and for those who are new at this stuff.

[@thomasharding1838]

I don't think that TCMath videos are for those who are new at this stuff, but for people who have been exposed to it but need some help in understanding it. Just solve the problem given and then fast forward to see if your answer is right and if so, go on to the next one. If your answer is wrong, watch the video to find out why. There is no legal requirement to watch the whole thing.

[@ndailorw5079]

…what’s the +/- for….? And “pi” is an unending decimal number and has nothing to do with roundness, necessarily. Maybe that’s one reason this instructor takes the time he does to explain the concepts behind these problems…? Wouldn’t hurt if he’d cut down the time a little, but he’s aware that others don’t understand and know as well as you do so he gets more involved….? Nothing wrong with that. Exercising a little more patience towards the uninitiated and the rusty wouldn’t hurt …or move on to something more challenging for you…..?

[@ECO473]

WHERE IS THIS RELEVANT IN NON-MATH, NON-STEM WORKING LIFE???

[@AnisYousuf-w8u]

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[@rontaylor3403]

12 what?

[@StephenRayWesley]

6224

[@patrickcorliss8878]

Old school trick. Double check the size. Whole square is 12 X 12 which is 144. Answer must be less than that.

[@rustyknott-W.D]

144 - 1/2 Area of the circle = 87.48, +/-. Pie are round, not square. Good grief. Again, you involve extra steps to solve a simple thing.

[@ndailorw5079]

One disease this guy has and is spreading is his deliberately leaving off the units in his final answers to area problems, and volume problems, like this one. To simply say x ≈ 87.48 is meaningless! 87.48 what ! He should always write the square units, or units^2, or cube units, or units^3 as he goes along working through the problem so as not to forget writing the units alongside the final answer as well. Because the units could be feet, inches, meters, millimeters, etc.! Who knows without specifying it! Even if no units are specified he still always give the general representation by writing units^2, or units^3 so as to at least imply dimension! It’s not a vacuum, or an empty space! It doesn’t do to simply write 87.48. 87.48 what? 87.48 in^2, 87.48 m^2, 87.48 units^2… what? On a real test he’d get points deducted for not having the units, in general or specific form, written down along with the at least the final answer.

[@kennethdias9988]

87.5

[@sekharb6651]

87.48

[@larrydickenson8922]

144 - 18pi

[@patrickcorliss8878]

Easy peasy.

[@Pulella100]

87.48