Inscribed Polygon Problems II

<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-inscribed-polygon-problems-ii" target="_blank">Inscribed Polygon Problems II Exercise</a></p><p>There&#39;s another thing to consider in this <strong><span style="color:#8e44ad;">Max Area of Inscribed Polygon II</span></strong> mountain entry.</p> <p>What if a square is inscribed in another square? How do we maximize its area? See if you can figure out with this diagram below.</p> <center><svg height="221.10000610351562" style=" width:661.6000366210938px; height:221.10000610351562px; background: #FFF; fill: none; " width="661.6000366210938" x="0" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" y="0"> <svg class="role-diagram-draw-area" xmlns="http://www.w3.org/2000/svg"><g class="shapes-region" style="stroke: black; fill: none;"><g class="composite-shape"><path class="real" d=" M29,20 L179.2,20 L179.2,170.2 L29,170.2 Z" style="stroke-width: 1; stroke: rgb(0, 0, 0); fill: none; fill-opacity: 1;"></path></g><g class="composite-shape"><path class="real" d=" M104.1,20.63 L178.57,95.1 L104.1,169.57 L29.63,95.1 Z" style="stroke-width: 1; stroke: rgb(74, 144, 226); fill: none; fill-opacity: 1; stroke-opacity: 1;"></path></g><g class="composite-shape"><path class="real" d=" M259,18 L409.2,18 L409.2,168.2 L259,168.2 Z" style="stroke-width: 1; stroke: rgb(0, 0, 0); fill: none; 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As we rotate the square to the right, the area has to get bigger for it to stay inscribed. It&#39;s not super obvious from the first to the second panel, but, as you can see, the third panel dramatically shows the area increase.&nbsp;</p> <p>To maximize the area of an inscribed square in another square, you simply have to make the inscribed square look more and more like the original square. This means that the <strong><span style="color:#e74c3c;">SMALLEST </span></strong>possible area for a square inscribed in another square is when the inscribed square&#39;s vertices are at the midpoints of the sides of the larger square.</p> <p>If that made no sense to you, don&#39;t worry. It was a hell of a sentence.</p> <p>In a nutshell, the smallest you can inscribe a square in another square is when the inside square is exactly half the area of the larger square.</p>