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.

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

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

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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