5 Circles and a Square
Geometry
Level
2
In the following diagram, the side length of the square is equal to 4 .
At π = 3.14, what is the gray shaded area subtracting from it the dark shaded area ?
The answer is 0.3.
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1 solution
The grey area at each corner is 4 1 ( 4 − π )
The black area is π − 4 4 1 ( 4 − π )
Total area of grey area minus black area is
1 2 ( 4 1 ( 4 − π ) ) − ( π − 4 4 1 ( 4 − π ) ) = 1 6 − 5 π
which, if π = 3 . 1 4 , works out to exactly 0 . 3