Viral Primary School Homework From Japan – Mind Your Decisions
A mother in Japan posted her child’s 6th grade math homework, after she found it too challenging to solve. The problem went viral after many adults were also unable to figure out the answer.
A square with a side length of 8 cm has two circular sectors at opposite corners, as shown. What is the area of the shaded region, which is the overlap of the two circular sectors?
As usual, watch the video for a solution.
Viral Primary School Homework From Japan
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Answer To Viral Primary School Homework From Japan
(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).
Many adults were confused because they were trying to remember a formula for the “almond” shape, and typically this is not a formula that is taught in school. However, the area of the almond shape can be solved using the areas of other figures that are taught. I will present two methods to solve for the area.
Method 1
Divide the almond shape in half, and that area is a circular segment, which is equal to the area of a circular sector minus the area of a right triangle. In this problem, the almond shape plus an isosceles right triangle have a total area equal to a quarter circle. Letting the side of the square be equal to r, the right triangle has an area of 0.5(r)(r)= 0.5r2 and the quarter circle has an area equal to 0.25πr2.
Subtracting the area of the triangle from both sides gives:
half almond area = 0.25πr2 – 0.5r2
Substitute r = 8 to get:
half almond area
= 0.25π(8)2 – 0.5(8)2
= 16π – 32
Doubling this value gives the area of the almond shape.
almond area
= 2(16π – 32)
= 32π – 64
≈ 36.53 cm2
Method 2
The interior of the square can be partitioned into 3 areas. Let the shaded area be b. The other two areas are equal by symmetry, so let their values be equal to a.
Then a + b + b + a will be the sum of the areas of two quarter circles, each with area 0.25π(8)2, so we have:
a + b + b + a
= 2(0.25π(8)2)
= 32π
We also have the area of the entire square is:
a + b + a = area square
a + b + a = 82 = 64
Subtracting this equation from the first gives:
a + b + b + a = 32π
– [a + b + a = 82 = 64]
b = 32π – 64 ≈ 36.53 cm2
And the area b exactly corresponds to the area to solve the question!
References
Threads
https://www.threads.com/@tanakasan_chi/post/DQ-vf45CbSC
Japanese articles (which I read with Google translate)
https://maidonanews.jp/article/16220522?p=30312645&ro=16220522&ri=0
https://news.livedoor.com/article/detail/30279313/
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