Homework In China – Solve For The Area In Red. Can You Solve It?

What is the total area of the red spots? The diagram involves a rectangle with dimensions of 10 and 20. Inside the rectangle one of its diagonals is connected. There are two circles of equal size that are tangent to each other and the rectangle. The video presents the solution to one version of the problem and then the solution to a second, much harder version, that was said to be assigned to 6th graders in China.

I read about this problem from Jin Yang on Twitter: https://twitter.com/jzy/status/759079328965505025

**Update 12 Aug: Many people suspected the second problem was too hard for 6th graders. It appears the first problem was assigned to 6th graders, and second problem (with the missing spot) was a misprint that went viral on social media. Jin Yang tweeted me with a link to the original problem assigned (in Chinese): http://wenku.baidu.com/view/de4510b0770bf78a652954a9.html

The Twitter thread from Jin Yang with the link to the original problem: https://twitter.com/jzy/status/763406201468047360

Blog post: http://wp.me/p6aMk-4Ls

There are other solution methods described on Quora: https://www.quora.com/What-is-the-area-of-the-shaded-part

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20 thoughts on “Homework In China – Solve For The Area In Red. Can You Solve It?

  1. Image in the thumbnail is wrong… The smallest part on the bottom right is not colored… It should be red too… It's all right in the video though :)

  2. Actually solve it within 6th math, draw a 90degree line in between two circle,then you will see a square and circle. 10^2-π5^2=100-25π=21.5 for all red.

    2nd question, draw a horizontal line at 5.
    1,one corner=21.5/4=5.35.
    2,Find the line inside the left circle. 30degree and right angle, the longest line is 10, so it is 5√3.
    1/3 of the triangle area in circle is (5√3)*(5/2)=12.5√3.
    The cut off circle area is 1/3(25π)-12.5√3.
    The area of the taken away red 1/2(5*10)-5.35-[1/3(25π)-12.5√3]
    =25-5.35-(26.17-12.5√3)
    =25-5.35-26.17+12.5√3
    =12.5√3-6.52=if you have a calculator, because √3, 6th grade was too far in my memory.
    The answer is 2nd question is
    21.5-(12.5√3-6.52)=28.02-12.5√3

  3. Area of rectangle = 200
    Area of the 2 circles = 2*3.14*5^2
    Area of red spots = (area of rect- area of 2 circles)/2
    Area of red spots = 21.5

  4. You could have split the orange triangle in two right triangles both similar to the larger one with a hypotenuse ot 5. Therefore the proportion of the areas would have been 5²:125=1:5 so the area of the orange triangle is 2*(1/5)*(5*10/2)=10.

  5. My solution:

    Square / 2 – area of one circle (because the circles are the same except flipped vertically)

    So 20*10=200
    200/2 = 100 (area of entire triangle)
    R = 10/2 = D/2 = 5
    R*R*Pi = 5*5*3.14 = 25*3.14=75 + 2,5 + 1 = 78,5

    100 – 78,5 = 21,5

    My answer is 21,5

  6. I am 13 years old and without reading any of the comments or watching the video, I've come up with the answer 21.46. Am I right?
    Edit: OMG I was exactly right!

  7. I dont get ur solution. You can just move the red region in the left corner to the complete the upper right, and cut a half of middle red region in the bottom and move it to the upper region.

    U just easily get the red region by
    Area of square – the area of the circle

  8. Boyali yerler birbirini tamamliyor. Olusan sekili Her kenari 10 cm olan bir karenin icine bir daire cizilmis ve o daireden 4 parca karenin 4 kenarinin orta noktalarına degiyor. Karenin alanindan karenin icindeki dairenin alanini cikarirsaniz sonucu bulursunuz. Bu arada kare nereden geldi burada dikdortgen var diye oracak olursaniz dikdortgenin uzun kenarinin ortasinda bir dikme indirin. Ortaya 2 kare cikiyor. Soruyu çözerken ortaya kare icerisindeki daire cikiyor

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