Can you find the area of the square inscribed in the hexagon?
<p>Given that the side length of a regular hexagon is 1, could you find the area of the square inscribed within it? This geometry problem was given to children between the ages of 14 and 18 to qualify for the BMO1 in the UK. Do you think you have what it takes to qualify for BMO1? Lets see!</p>
<p>First, we “zoom in” onto the hexagon and focus on just one corner of it. That is, the following region:</p>
<p><img alt="" src="https://miro.medium.com/v2/resize:fit:700/1*0VOnsYrKutEz33DfvrS76w.png" style="height:700px; width:700px" /></p>
<p>If we manage to find the side of the square, we are basically done. we will now relabel everything slightly. Suppose that the square has side length 2x. Then we can write label everything as follows, since we are essentially halving the square. We also have a + b = 1 since the side length of the hexagon is 1.</p>
<p><a href="https://medium.com/wojciechs-maths-problems/can-you-find-the-area-of-the-square-inscribed-in-the-hexagon-9eaceb92aa85"><strong>Read More</strong></a></p>