Max Area Regardless of Shape
<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-max-area-regardless-of-shape" target="_blank">Max Area Regardless of Shape Exercise</a></p><p>If I provided you with $60$ feet of rope and told you to use that rope to enclose the largest area possible, what shape would you make? How would you <strong><span style="color:#8e44ad;">Maximize the Area Regardless of Shape</span></strong>?</p>
<p>Would you make a triangle? A square? A regular hexagon? A $100$-sided regular polygon? What?!</p>
<p><strong><span style="color:#27ae60;">Perhaps this graphic can help</span></strong>. Note that the perimeter of each regular polgyon is $60$.</p>
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<p>What do you notice? As we increase the number of sides of these regular polygons (and keep the perimeter constant at $60$), what happens to the area? </p>
<p style="text-align: center;"><span style="color:#e74c3c;">It <span style="font-size:16px;">gets</span> <span style="font-size:24px;">larger!</span> <span style="font-size:28px;">Whoa!</span></span></p>
<p>If we take this to its logical conclusion, the shape that produces the largest area with our $60$ feet of rope is...<strong><span style="color:#27ae60;">A CIRCLE</span></strong>!</p>
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<p><strong><span style="color:#e74c3c;">NOTE</span>: </strong>We will learn the area of a circle soon enough. Soon enough padawan. Soon enough.</p>