Area of this Rectangle

[Blaze_Raven]

If there's one thing I have learnt, it's that there is always a right angled triangle whenever the balls touch.

[scottsweet]

The problem solving (not just the math) in your content is next level

[nikshepta]

The second reason why I watch till the end is to hear "How exciting"😂
Math being the first one

[electrofrost]

for those wondering the area without the root is 14.928 sq. cm

[resyntax]

Remember: if you're doing anything geometry related, the Pythagorian Theorum will save your ass.

[Eagle_SFM]

My attempt: look at it for about 8 seconds, "ehhh about 15".

Turns out it's 14.93

[FurbleBurble]

This channel doesn't just teach me math. It also teaches me to approach problems in ways that I'd never consider on my own. I think this is fantastic. I never made it to Algebra 2 in high school before quitting. I did somehow place into Algebra 3 at my local community college and got out with an A, an A that I lost a lot of sleep trying to earn. I love math, but I hate school. Resources like this channel are great. Thank you.

[badlydrawnjolteon]

this is the first one i was able to solve myself, and i did it instantly, i knew that the distance through the circles was pretty much the only thing we knew, so when i drew it out in my head i recognized the diagonol as a hypotenuse, made the triangle and knew the answer. very proud

[ftrctyvreycertcewtcwrgcwef]

Very straight to the point
Very straight forward
Very nice video
👍

[PerunaMuayThai]

I haven't been in a class since 2011 and that was end level computer science so it's been even longer since I had to look at this stuff... yet I'm super engaged with this channel content lol

[matthewpatrick]

Love the “how exciting” tag as the end of all your videos. Lol

[casmartin]

I know absolutely nothing about maths beyond the basics but this is the 4th video of yours that I've watched and I must really be learning a lot from you as I actually figured this one out for the most part, so thank you 👍🏾🙏🏾

[corporeal]

From watching a bunch of your other videos, the tools learned helped me solve this while paused at the start. I can't stress how excited I am

[drmilkweed]

my solution involved seeing that the centers of the circles formed an equilateral triangle, then cutting that in half to make a 30/60/90 right triangle with two known side lengths. yours was a lot less complicated!

[sacrilegiousboi]

Engineers getting an aneurysm looking at the final answer.

[DGarrettDG]

i appreciate that these videos get to the point and explain the process. i want to study math again and this is waking my brain up

[usedcars]

The thumbnail made me think this was a Terry A Davis video 💀

[ThatNiceDutchGuy]

Question, clear explanation, no fluff! Much appreciated.

[OptimusPhillip]

My attempt:
The width of the rectangle is equal to the sum of the diameters of the top two circles. Radius of 1 means diameter of 2, 2*2=4, so the width is 4.
The height, meanwhile, is equal to the radius of the top two circles, plus the height of the triangle formed by the centers of the three circles, plus the radius of the bottom circle.
That triangle is an equilateral triangle with side length 2cm. Thus, its height is 2sin(60), or sqrt(3). The radius of all three circles is 1, so that's 1+sqrt(3)+1, or 2+sqrt(3).
Area is width times height, so the area of the rectangle is 4(2+sqrt(3)), or 8+4sqrt(3)

[dw]

When adding a unit, this is actually a multiplication. So the result is not 8 + 4 * SQRT(3) cm² but either 8 cm² + 4 * SQRT(3) cm² or alternativly [8 + 4 * SQRT(3)] cm² . Otherwise you would add a scalar to an area, which is rather awkward.