This geometry problem was asked to students in Singapore. What is the area of the shaded region? The figure is composed of squares with side length 4 and quarter circles.
Watch the video for a solution.
Can You Solve This Geometry Problem From Singapore? The Area Of A Claw
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Answer To Geometry Problem From Singapore
I first approached the problem by considering the area of a quarter circle and then subtracting out shapes in order to find the area of the shaded region.
The answer is 32π – 64.
But there is a much more elegant solution! The key is considering the diagonal of the 3×3 grid. The upper region can be rotated about the center to join with the lower region. The resulting shape is a segment of a quarter circle that has a segment of a smaller quarter circle removed.
The area of a segment of a quarter circle is the area of a quarter circle minus the area of an isosceles right triangle. If the radius r, the area is πr2/4 – r2/2.
The larger circular segment has radius 12, and the smaller one has radius 4. So we can calculate the area:
We get to the answer 32π – 64 in a much more direct manner.
Sources
PLSE style circle problem (Mindscope Khoo channel)
https://www.youtube.com/watch?v=yb_JUZFKi-A
Challenging area question – 4 quarter circles and square
http://studyroom.sg/12/
Read the full article here by Mind Your Decisions
1 comment:
This geometry challenge is an excellent example of how elegant mathematical problems can inspire creative thinking beyond routine formulas. The clear presentation encourages readers to analyze patterns, test logical approaches, and appreciate the beauty of geometric reasoning. It's the kind of puzzle that not only sharpens problem-solving skills but also reminds us why mathematics remains both intellectually rewarding and enjoyable.
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