Are You Smart Enough To Find The Area?

An Interesting Geometry Puzzle

There are four circles of radius 1, which are each tangent to two sides of a square and externally tangent to a circle of radius 2.

So long you know some basic geometry and have some imagination, you will be able to crack this puzzle 🧩

Here’s a hint: connect the circles …

I recommend you pause the article, grab your pen and paper, and give this a go. When you are ready, keep reading for the solution! ✒️

Solution

We let s be the length of a side of the square.

We then construct an isosceles right triangle with vertices at the centers of the circle of radius 2 and two of the circles of radius 1.

This triangle has legs of length 3.

Using Pythagoras’ Theorem, we have h² = 3² + 3²

So the hypotenuse has length 3√2.

The length of a side of the square is 2 more than the length of this hypotenuse, as indicated by the two blue arrows below.

So we have the side length of the square as

Squaring it, we get

And that’s the area.

How amazing 👧

What was your thought process this time? Comment down below, I am eager to know :) 💞

Save and share the following list for the best math puzzles on Medium👇

Thank you for reading. Don’t forget to clap the article if you find it insightful.

I put a lot of effort into writing every article for you, so please buy me a coffee☕ if you are feeling generous. It’s a great way to support my writing as well as my personal and academic life.

Love, Bella ❤️