Find the area of the shaded region in the inscribed circle on square

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SUMMARY

The discussion focuses on calculating the area of the shaded region in a circle inscribed within a square. Key calculations include the area of the minor sector, major sector, and triangle, leading to the final area of the shaded region. The minor sector is calculated as Aminor sector = 27.947 cm2, the triangle as Atriangle = 9.8366 cm2, and the major sector as Amajor sector = 50.592 cm2. The final area of the shaded region is determined to be approximately 14.64 cm2.

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  • Understanding of circular geometry and sector area calculations
  • Familiarity with trigonometric functions and their applications in geometry
  • Knowledge of integration techniques for area calculations
  • Ability to apply the Pythagorean theorem in geometric contexts
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  • Learn about circular segment area calculations using the formula A = R2(θ - 0.5 sin(2θ))
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Mathematicians, geometry enthusiasts, educators, and students looking to deepen their understanding of area calculations in circular and polygonal shapes.

  • #31
chwala said:
Eieeeh! Brilliant mate.
Thanks for the kind compliment but if truth be told I think the method more or less duplicates that in post #15. It is just that PF user @PeroK actually evaluated the integral whereas I took the lazy guy solution of sending it off to Wolfram Alpha!
 

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