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599 lines
18 KiB
HTML
599 lines
18 KiB
HTML
<!doctype html>
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<html lang="en">
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<!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/geometry/polygons.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:38:07 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<title>Polygons</title>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Polygons</h1>
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<h3 align="center"><img src="images/polygon-mosaic.jpg" width="624" height="145" alt="polygon mosaic" /><br>
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A polygon is a <a href="plane.html">plane</a> shape with straight sides.</h3>
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<h2>Is it a Polygon?</h2>
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<p>Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (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/pentagon-irregular.svg" alt="pentagon irregular" /></b></td>
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<td><b><img src="images/pentagon-not.svg" alt="not a pentagon (curve)" /></b></td>
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<td><b><img src="images/pentagon-not2.gif" width="83" height="87" alt="not a pentagon (open)" /></b></td>
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</tr>
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<tr align="center">
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<td><b>Polygon</b><br>
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(straight sides)</td>
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<td><b>Not</b> a Polygon<br>
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(has a curve)</td>
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<td><b>Not</b> a Polygon<br>
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(open, not closed)</td>
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</tr>
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</table>
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<div class="words">
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<p><b>Polygon</b> comes from Greek. <b>Poly-</b> means "many" and <b>-gon</b> means "angle".</p>
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</div>
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<h2>Types of Polygons</h2>
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<h3>Regular or Irregular</h3>
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<p>A <b>regular</b> polygon has all angles equal and all sides equal, otherwise it is<b> irregular</b></p>
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<table style="border: 0; margin:auto;">
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<tr align="center">
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<td><b><img src="images/pentagon-regular.svg" alt="pentagon regular" /></b></td>
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<td width="40"> </td>
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<td><b><img src="images/pentagon-irregular.svg" alt="pentagon irregular" /></b></td>
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</tr>
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<tr align="center">
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<td>Regular</td>
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<td> </td>
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<td>Irregular</td>
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</tr>
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</table>
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<p> </p>
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<h3>Concave or Convex</h3>
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<p>A <b>convex</b> polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.</p>
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<p>If any internal angle is greater than 180° then the polygon is <b>concave</b>. (<i>Think: concave has a "cave" in it</i>)</p>
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<table style="border: 0; margin:auto;">
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<tr align="center">
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<td><b><img src="images/pentagon-irregular.svg" alt="pentagon irregular" /></b></td>
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<td width="40"> </td>
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<td><b><img src="images/pentagon-irregular-concave.svg" alt="pentagon concave" /></b></td>
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</tr>
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<tr align="center">
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<td>Convex </td>
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<td> </td>
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<td>Concave</td>
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</tr>
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</table>
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<p> </p>
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<h3>Simple or Complex</h3>
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<p>A <b>simple</b> polygon has only one boundary, and it doesn't cross over itself. A <b>complex</b> polygon intersects itself! Many rules about polygons don't work when it is complex.</p>
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<table style="border: 0; margin:auto;">
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<tr align="center">
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<td><b><img src="images/pentagon-irregular.svg" alt="pentagon irregular" /></b></td>
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<td width="40"> </td>
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<td><b><img src="images/pentagon-complex.gif" width="110" height="100" alt="pentagon complex" /></b></td>
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</tr>
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<tr align="center">
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<td>Simple Polygon<br>
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(this one's a Pentagon)</td>
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<td> </td>
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<td>Complex Polygon<br>
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(also a Pentagon) </td>
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</tr>
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</table>
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<p> </p>
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<h2>More Examples</h2>
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<table style="border: 0; margin:auto;">
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<tr align="center">
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<td><b><img src="images/hexagon-irregular.svg" alt="hexagon irregular" /></b></td>
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<td width="30"> </td>
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<td><b><img src="images/concave-octagon.gif" width="110" height="100" alt="concave octagon" /></b></td>
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<td width="30"> </td>
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<td><b><img src="images/star-polygon.gif" width="110" height="100" alt="star polygon" /></b></td>
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</tr>
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<tr align="center">
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<td><b>Irregular Hexagon</b><br>
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<br>
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</td>
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<td> </td>
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<td><b>Concave Octagon<br>
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</b><br>
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</td>
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<td> </td>
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<td><b>Complex Polygon</b><br>
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(a "star polygon",<br>
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in this case a <a href="pentagram.html">pentagram</a>)</td>
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</tr>
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</table>
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<p> </p>
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<p><span style="float:left; margin: 10px;"><a href="polygons-interactive.html"><img src="images/polygons-interactive-thumb.gif" width="100" height="100" border="0" alt="polygons interactive" /></a></span></p>
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<h2>Play With Them!</h2>
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<p>Try <a href="polygons-interactive.html">Interactive Polygons</a> ... make them regular, concave or complex.</p>
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<p> </p>
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<h2>Names of Polygons</h2>
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<div class="simple">
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<table width="90%" border="0" align="center">
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<tr>
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<td height="14" bgcolor="#FFFFFF"> </td>
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<td height="14" bgcolor="#FFFFFF"> </td>
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<td height="14" colspan="2" align="center">If it is a <b>Regular Polygon</b>...</td>
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</tr>
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<tr align="center">
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<th>Name</th>
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<th>Sides</th>
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<th>Shape</th>
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<th>Interior Angle</th>
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</tr>
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<tr align="center">
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<td><a href="../triangle.html">Triangle</a> <i>(or Trigon)</i></td>
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<td><b>3</b></td>
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<td><img src="images/triangle-regular.svg" height="50" alt="regular triangle" /></td>
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<td>60°</td>
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</tr>
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<tr align="center">
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<td><a href="../quadrilaterals.html">Quadrilateral</a> <i>(or Tetragon)</i></td>
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<td><b>4</b></td>
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<td><img src="images/quadrilateral-regular.svg" height="50" alt="regular quadrilateral" /></td>
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<td>90°</td>
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</tr>
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<tr align="center">
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<td><a href="pentagon.html">Pentagon</a></td>
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<td><b>5</b></td>
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<td><b><img src="images/pentagon-regular.svg" height="50" alt="pentagon regular" /></b></td>
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<td>108°</td>
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</tr>
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<tr align="center">
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<td><a href="hexagon.html">Hexagon</a></td>
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<td><b>6</b></td>
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<td><b><img src="images/hexagon-regular.svg" alt="hexagon regular" height="50" /></b></td>
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<td>120°</td>
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</tr>
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<tr align="center">
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<td>Heptagon <i>(or Septagon)</i></td>
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<td><b>7</b></td>
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<td><b><img src="images/heptagon-regular.svg" alt="heptagon refular" height="50" /></b></td>
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<td>128.571°</td>
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</tr>
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<tr align="center">
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<td><a href="octagon.html">Octagon</a></td>
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<td><b>8</b></td>
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<td><b><img src="images/octagon-regular.svg" alt="octagon regular" height="50" /></b></td>
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<td>135°</td>
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</tr>
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<tr align="center">
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<td>Nonagon <i>(or Enneagon) </i></td>
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<td><b>9</b></td>
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<td><img src="images/nonagon-regular.svg" alt="nonagon regular" height="50" /></td>
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<td>140°</td>
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</tr>
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<tr align="center">
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<td>Decagon</td>
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<td><b>10</b></td>
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<td><img src="images/decagon-regular.svg" height="50" alt="regular decagon" /></td>
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<td>144°</td>
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</tr>
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<tr align="center">
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<td>Hendecagon <i>(or Undecagon)</i></td>
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<td><b>11</b></td>
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<td><img src="images/hendecagon-regular.svg" height="50" alt="regular hendecagon" /></td>
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<td>147.273°</td>
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</tr>
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<tr align="center">
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<td>Dodecagon</td>
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<td><b>12</b></td>
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<td><img src="images/dodecagon-regular.svg" height="50" alt="regular dodecagon" /></td>
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<td>150°</td>
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</tr>
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<tr align="center">
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<td>Triskaidecagon </td>
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<td><b>13</b></td>
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<td> </td>
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<td>152.308°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Tetrakaidecagon </td>
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<td><b>14</b></td>
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<td> </td>
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<td>154.286°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Pentadecagon</td>
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<td><b>15</b></td>
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<td> </td>
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<td>156°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Hexakaidecagon </td>
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<td><b>16</b></td>
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<td> </td>
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<td>157.5°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Heptadecagon</td>
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<td><b>17</b></td>
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<td> </td>
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<td>158.824°<br>
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</td> </tr>
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<tr align="center">
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<td>Octakaidecagon </td>
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<td><b>18</b></td>
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<td> </td>
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<td>160°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Enneadecagon</td>
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<td><b>19</b></td>
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<td> </td>
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<td>161.053°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Icosagon</td>
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<td><b>20</b></td>
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<td> </td>
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<td>162°<br>
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</td>
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</tr>
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<tr align="center">
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<td height="14">Triacontagon</td>
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<td height="14"><b>30</b></td>
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<td height="14"> </td>
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<td height="14">168°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Tetracontagon </td>
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<td><b>40</b></td>
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<td> </td>
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<td>171°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Pentacontagon</td>
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<td><b>50</b></td>
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<td> </td>
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<td>172.8°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Hexacontagon </td>
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<td><b>60</b></td>
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<td> </td>
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<td>174°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Heptacontagon </td>
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<td><b>70</b></td>
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<td> </td>
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<td>174.857°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Octacontagon </td>
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<td><b>80</b></td>
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<td> </td>
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<td>175.5°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Enneacontagon </td>
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<td><b>90</b></td>
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<td> </td>
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<td>176°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Hectagon</td>
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<td><b>100</b></td>
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<td> </td>
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<td>176.4°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Chiliagon</td>
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<td><b>1,000</b></td>
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<td> </td>
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<td>179.64°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Myriagon</td>
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<td><b>10,000</b></td>
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<td> </td>
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<td>179.964°<br>
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</td>
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</tr>
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<tr align="center">
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<td>Megagon</td>
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<td><b>1,000,000</b></td>
|
|
<td> </td>
|
|
<td>~180°</td>
|
|
</tr>
|
|
<tr align="center">
|
|
<td>Googolgon</td>
|
|
<td><b>10<sup>100</sup></b></td>
|
|
<td> </td>
|
|
<td>~180°</td>
|
|
</tr>
|
|
<tr align="center">
|
|
<td>n-gon</td>
|
|
<td><b>n</b></td>
|
|
<td><img src="images/n-gon-regular.svg" height="50" alt="regular n gon" /></td>
|
|
<td>(<b>n</b>−2) × 180<b>°</b> / <b>n</b></td>
|
|
</tr>
|
|
</table>
|
|
</div><br>
|
|
<p>You can make names using this method:</p>
|
|
<table border="0" align="center" cellpadding="0" cellspacing="0">
|
|
<tr>
|
|
<td valign="top">
|
|
<table style="border: 0;">
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>Sides</b></div>
|
|
</td>
|
|
<td align="right"> </td>
|
|
<td align="right">Start with...</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>20</b></div>
|
|
</td>
|
|
<td align="right"> </td>
|
|
<td align="right">Icosi...</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>30</b></div>
|
|
</td>
|
|
<td align="right"> </td>
|
|
<td align="right">Triaconta...</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>40</b></div>
|
|
</td>
|
|
<td align="right"> </td>
|
|
<td align="right">Tetraconta...</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>50</b></div>
|
|
</td>
|
|
<td align="right"> </td>
|
|
<td align="right">Pentaconta...</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>60</b></div>
|
|
</td>
|
|
<td align="right"> </td>
|
|
<td align="right">Hexaconta...</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>70</b></div>
|
|
</td>
|
|
<td align="right"> </td>
|
|
<td align="right">Heptaconta...</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>80</b></div>
|
|
</td>
|
|
<td align="right"> </td>
|
|
<td align="right">Octaconta...</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>90</b></div>
|
|
</td>
|
|
<td align="right"> </td>
|
|
<td align="right">Enneaconta...</td>
|
|
</tr>
|
|
<tr>
|
|
<td align="center"><b>100</b></td>
|
|
<td align="right"> </td>
|
|
<td align="right">Hecta...</td>
|
|
</tr>
|
|
<tr>
|
|
<td align="center"><b>etc..</b></td>
|
|
<td align="right"> </td>
|
|
<td align="right"> </td>
|
|
</tr>
|
|
</table>
|
|
</td>
|
|
<td width="30">
|
|
<div class="center"><img src="../images/style/right-arrow.gif" width="46" height="46" alt="right arrow" /></div>
|
|
</td>
|
|
<td>
|
|
<table style="border: 0;">
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>Sides</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...end with</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>+1</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...henagon</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>+2</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...digon</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>+3</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...trigon</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>+4</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...tetragon</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>+5</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...pentagon</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>+6</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...hexagon</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>+7</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...heptagon</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>+8</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...octagon</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<div class="center"><b>+9</b></div>
|
|
</td>
|
|
<td> </td>
|
|
<td>...enneagon</td>
|
|
</tr>
|
|
</table>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td colspan="3" valign="top">
|
|
<p>Example: a 62-sided polygon is a Hexacontadigon</p>
|
|
</td>
|
|
</tr>
|
|
</table>
|
|
<div class="words">
|
|
<p>BUT, for polygons with 13 or more sides, it is OK (and easier) to write "<b>13-gon</b>", "<b>14-gon</b>" ... "<b>100-gon"</b>, etc.</p>
|
|
</div>
|
|
<h2>Remembering</h2>
|
|
<h3>Quadrilateral (4 Sides)</h3>
|
|
<p class="center"><img src="images/quad-bike.jpg" width="212" height="160" alt="quad bike" /><br>
|
|
A <b>Quad</b> Bike has 4 wheels</p>
|
|
<h3>Pentagon (5 Sides)</h3>
|
|
<p class="center"><img src="images/pentagon-building2.jpg" width="536" height="327" alt="pentagon building" /><br>
|
|
The "<b>Pentagon</b>" in Washington DC has 5 sides</p>
|
|
<h3>Hexagon (6 Sides)</h3>
|
|
<p class="center"><img src="images/honeycomb2.jpg" width="300" height="219" alt="honeycomb" /><br>
|
|
<b>H</b>oneycomb has <b>H</b>exagons</p>
|
|
<h3>Septagon (7 Sides)</h3>
|
|
<p class="center">Think <b>Sept</b>agon is a <b>"Seven-</b>agon"</p>
|
|
<h3>Octagon (8 Sides)</h3>
|
|
<p class="center"><img src="images/octopus.jpg" width="180" height="195" alt="octopus" /><br>
|
|
An <b>Octo</b>pus has 8 tentacles</p>
|
|
<h3>Nonagon (9 Sides)</h3>
|
|
<p class="center">Think <b>Non</b>agon is a <b>"Nine-</b>agon"</p>
|
|
|
|
<h3>Decagon (10 Sides)</h3>
|
|
<p class="center">Think <b>Dec</b>agon has 10 sides,<br>
|
|
just like our <b>Dec</b>imal system has 10 digits</p>
|
|
<p> </p>
|
|
<div class="questions">
|
|
<script>
|
|
getQ(629, 630, 633, 634, 2125, 2126, 3255, 3256, 2127, 3257);
|
|
</script> </div>
|
|
|
|
<div class="related">
|
|
<a href="polygons-interactive.html">Interactive Polygons</a>
|
|
<a href="interior-angles-polygons.html">Interior Angles of Polygons</a>
|
|
<a href="exterior-angles-polygons.html">Exterior Angles of Polygons</a>
|
|
<a href="../shape.html">2D Shapes (simpler page)</a>
|
|
</div>
|
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