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Geometry of Plane figures | Pre-RMO 2019

Try this beautiful problem from Pre-RMO, 2019 based on Geometry of plane figures.

Geometry of Plane figures - Pre-RMO 2019


From a square with sides of length 5, triangular pieces from the four corners are removed to form a regular octagon. Find the area removed to the nearest integer.

  • 1
  • 2
  • 3
  • 4

Key Concepts


Area of Plane figures

Algebra

Approximation in number theory

Check the Answer


Answer: 4.

Pre-RMO, 2019

Geometry Revisited by Coxeter .

Try with Hints


First hint

A figure is taken such that side of triangle is x and sides of octagon are $x\sqrt 2$ and $5-2x$

Second Hint

Geometry of plane figures

Here $5-2x$=$x\sqrt 2$ then x=$\frac{5}{2+\sqrt 2}$

Final Step

Area removed =2x^2=$\frac{2(25)}{2(1+2^\frac{1}{2})}$ which is nearly 4.3 then the nearest integer is 4

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