Find the Blue Area

For more geometry challenges check out the above link!

[mrmemer]

I’m going to take off half a point from this question on the test because the unit is centimeters was included and you didn’t specify in your answer

[brbailey]

The rotating of r1 and r2 to form the hypotenuse blew my mind. I gasp aloud.

[esunisen]

Unit of rectangle side: cm

Andy: We don't use this in the US.

[bangsulthon]

Man, i randomly found your channel and now i'm addicted to it... It's remind me the fun of math that i forget decades ago... Massive thanks...

[JohnnyOU]

I love this channel. There is zero fat on these videos. You just shred through these math problems. Keep 'em coming!

[kidneybeans]

at 2:14 you already have the value for r1^2. you could have just plugged it in to 3pi(r1)^2/2. No need to take the extra step of square rooting it, then plugging it back in only to square it again. Great vid BTW

[afinger]

Did anyone else use Trigonometry? I seen the right angle triangle of 4(adjacent), r(opposite) and 3r(hypotenuse)...

So sinA=r/3r

SinA=1/3 (r cancelled top and bottom)

A=sin^-1(1/3)

TanA=r/4

So, r=4TanA

r = √2 and then continue on with Area formula for the half and quarter circles.... Love the puzzles and seeing how we differ in solution.

[NightSkyJeff]

To save a step or two, you don't need to know the value of r{1}, you need to know the value of (r{1})^2, and you figure that out when you solve the triangle.

[michaellacaria]

Wish i had these animations and explanations 40yrs ago! 😊

[MiniNoahTheWorm]

I didn't think connecting the two radiuses to form the triangle was an option because I couldn't convince myself that they would perfectly align

[Peter_Riis_DK]

Well done, but I believe the unit is cm...

[karl]

You bring so many interesting questions. Nice contents!

[hephi]

Im curious how one can find that r1 and r2 can make that triangle? is there a proof of it somewhere?

[samuelking]

How do we know for sure that the r1 + r2 hypotenuse is actually linear/the angle between the connected radii is 180 degrees? Is there some mathematical principle that if two circles are tangent to each other, the line between their centers will necessarily run through the point of tangency?

[muhammadfaris]

How do you know the hyphotenuse of the triangle will intersect (touch) the center of the two circles? In other word, how do you know R1 and R2 can be in straight line to form a hyphotenuse for the triangle? Thank you.

[memesalldayjack]

I'm not smart enough to confirm whether those answers are correct, I'm also not in the mood to pay very close attention to it all, but i like watching it, cause i see small things that'll probably help me someday, like thinking about making a triangle with that radius

[Kagetra]

What a great subscription your channel is! I love these fun little easy problems, but I'd never make time for them without your new videos in my feed to remind me. The ones where your solution is quite different than mine are a special treat.

[NatashaRomanoffThailand]

Why is the unit of the answer is u^2? Should it be cm^2 because the picture already shows 4cm?

[eve_the_eevee_rh]

Insert filler text claiming spoilers



Let the radius of the semicircle be x. The radius of the quartercircle is twice the semicircle, so its radius is 2x.
Drawing a line connecting the centers of the circles, we can use the Pythagoras Theorem to derive the following equation:
4² + x² = (x + 2x)²
16 + x² = 9x²
8x² = 16
x² = 2

pi(r)²
½pi(x²) + ¼pi(2x)²
= ½pi(x²) + ¼pi*4x²
= ½pi(x²) + pix²
= 1½pix²
= 1½pi(2)
= 3pi
≈9.4247

[PatentDude]

I just subscribed to your channel. How exciting!