Select Page

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

But try the problem first…

Source

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

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