Cut it off and join, without gaps and overlapping

Geometry Level 1

Each of the circles in figure 1 is of radius 10. After some cutting, there are 5 identical shapes, which can be fitted together without gaps and overlapping. What is the total area of the shape in figure 2?


The answer is 1000.

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2 solutions

Chan Lye Lee
Jun 21, 2020

From the figure A above, we can fill the gaps (in squares) using the shapes outside the squares. We then obtain 5 squares in figure B, which each of side length 10 2 10 \sqrt{2} . Hence the area of each square is 100 × 2 = 200 100 \times 2 = 200 . Therefore the total area of the shape in figure 2 (in the question) is 5 × 200 = 1000 5 \times 200 = \boxed{1000} .

Nice re-arrangement! +1

Mahdi Raza - 11 months, 3 weeks ago

Area of each circle is 100 π 100π . Area of the cut off region from each circle is 100 π 200 100π-200 . So the area of the remaining portion of each circle is 200 200 . There are five such figures in shape 2 2 , whose total area is 5 × 200 = 1000 5\times 200=\boxed {1000} .

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