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


But try the problem first…

Answer: 4.

Source
Suggested Reading

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$2^\frac{1}{2}$ and 5-2x

Second Hint

Geometry of plane figures

Here 5-2x=x$2^\frac{1}{2}$ then x=$\frac{5}{2+2^\frac{1}{2}}$

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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