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167 lines
7.7 KiB
HTML
167 lines
7.7 KiB
HTML
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<!-- Mirrored from www.mathsisfun.com/geometry/hexagon.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:42:50 GMT -->
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<head>
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<title>Hexagon</title>
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Hexagon</h1>
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<p class="center">A hexagon is a 6-sided <a href="polygons.html">polygon</a> (a flat shape with straight sides). </p>
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<script type="text/javascript">areacoordsMain('6');</script>
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<p class="center"><img src="images/soap-bubbles-hexagon.jpg" width="246" height="178" alt="soap bubbles hexagons" /><br>
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Soap bubbles tend to form hexagons<br>
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when they join up.</p>
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<p class="center"><img src="images/honeycomb2.jpg" width="300" height="219" alt="honeycomb hexagons" /><br>
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Honeycomb has hexagons too!</p>
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<h2>Regular or Irregular</h2>
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<p>When all angles are equal and all sides are equal it is <b>regular</b>, otherwise it is<b> irregular</b>:</p>
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<table width="60%" border="0" align="center">
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<tr align="center">
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<td><b><img src="images/hexagon-regular.svg" alt="Regular Hexagon" /></b></td>
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<td><b><img src="images/hexagon-irregular.svg" alt="Irregular hexagon" /><img src="images/hexagon-irregular-concave.svg" alt="Irregular hexagon" /></b></td>
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</tr>
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<tr align="center">
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<td>Regular Hexagon</td>
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<td>Irregular Hexagons</td>
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</tr>
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</table>
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<h2>Concave or Convex</h2>
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<p>A <b>convex</b> <span class="center">hexagon</span> has no angles pointing inwards. More precisely, no internal angles can be more than 180°. </p>
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<p>When any internal angle is greater than 180° it is <b>concave</b>. (<i>Think: concave has a "cave" in it</i>)</p>
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<table width="60%" border="0" align="center">
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<tr align="center">
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<td><b><img src="images/hexagon-irregular.svg" alt="Irregular hexagon" /></b></td>
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<td><b><img src="images/hexagon-irregular-concave.svg" alt="Irregular hexagon" /></b></td>
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</tr>
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<tr align="center">
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<td>Convex <span class="center">Hexagon</span></td>
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<td>Concave <span class="center">Hexagon</span></td>
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</tr>
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</table>
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<h2>Is it a Hexagon?</h2>
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<p>No curved sides. And the shape must also be <b>closed</b> (all the lines connect up):</p>
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<table width="80%" border="0" align="center">
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<tr align="center">
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<td><b><img src="images/hexagon-irregular.svg" alt="Irregular hexagon" /></b></td>
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<td><b><img src="images/hexagon-not.svg" alt="Not a Hexagon" /></b></td>
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<td><b><img src="images/hexagon-not2.gif" alt="Not a Hexagon " width="86" height="91" /></b></td>
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</tr>
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<tr align="center">
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<td><b>Hexagon</b><br />
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(straight sides)</td>
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<td><b>Not</b> a Hexagon <br />
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(has a curve)</td>
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<td><b>Not</b> a Hexagon <br />
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(open, not closed)</td>
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</tr>
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</table>
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<h2>Properties</h2>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/hexagon-regular.svg" alt="Regular Hexagon" /></p>
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<p>A <b>regular</b> hexagon has:</p>
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<ul>
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<li><a href="interior-angles-polygons.html">Interior Angles</a> of <b>120°</b></li>
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<li><a href="exterior-angles-polygons.html">Exterior Angles</a> of <b>60°</b></li>
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<li>Area = <b>(1.5√3) × s<sup>2</sup></b> , or approximately <b>2.5980762 × s<sup>2</sup></b> (where s=side length)</li>
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<li>Radius equals side length </li>
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</ul>
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<p class="center"><img src="images/hexagon-regular-radius.svg" alt="Regular Hexagon radius of side length" /><br>
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The radius is the side length.<br>
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It is also made of 6 regular triangles!</p>
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<p><b>Any</b> hexagon has:</p>
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<ul>
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<li>Sum of Interior Angles of <b>720°</b></li>
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<li>9 <a href="polygons-diagonals.html">diagonals</a></li>
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</ul>
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<h2>More Images</h2>
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<p class="center"><img src="images/nuts-bolts.jpg" width="240" height="237" alt="Hex nuts and bolts"><br>
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Hexagonal nuts and bolts are easy to grip with a wrench, <br>
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which can be re-positioned every 60° if needed.</p>
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<p> </p>
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<p class="center"><img src="images/saturn-hexagon.jpg" width="300" height="207" alt="Hexagon on Saturn"><br>
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There is a <b>huge</b> hexagon on Saturn, <br>
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it is wider than Earth.</p>
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<p class="center"><img src="images/saturn-hexagon2.jpg" width="540" height="256" alt="Hexagon on Saturn"><br>
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Another image of the hexagon on Saturn.</p>
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<p class="center"><img src="images/snowflake1.jpg" width="361" height="390" alt="Snowflake with Hexagonal pattern"><br>
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Snowflakes have hexagonal patterns, like this beautiful image from NASA.<br>
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<i>Photograph by NASA / Alexey Kljatov.</i></p>
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<p class="center"><img src="images/snowflake2.jpg" width="359" height="384" alt="Hexagonal Ice Crystal"><br>
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Also a snowflake! <i><br>
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Photograph by NASA / Alexey Kljatov.</i></p>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(4891, 629, 676, 758, 782, 3261, 3260, 633, 6069, 2884);</script>
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</div>
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<div class="related"><a href="index.html">Geometry Index</a></div>
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Copyright © 2018 MathsIsFun.com
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