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

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

Area of Plane figures

Algebra

Approximation in number theory

But try the problem first...

Answer: 4.

Source

Suggested Reading

Pre-RMO, 2019

Geometry Revisited by Coxeter .

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

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

- https://www.cheenta.com/gaps-in-permutation-tomato-objective-problem/
- https://www.youtube.com/watch?v=z9az0oHnQxk

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