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.
Area of Plane figures
Algebra
Approximation in number theory
Answer: 4.
Pre-RMO, 2019
Geometry Revisited by Coxeter .
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
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
