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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

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

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