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<title>Pyramids</title>
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<h1 align="center">Pyramids</h1>
<p class="center"><img src="images/pyramids.jpg" style="max-width:100%" alt="Great Pyramids of Egypt" /></p>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/pyramid-outlined.jpg" width="220" height="148" alt="Pyramid Outlined" /></p>
<p>When we think of pyramids we think of the <b>Great Pyramids of Egypt</b>. </p>
<p>They are actually <i><b>Square Pyramids</b></i>, because their base is a Square.</p>
<h2>Parts of a Pyramid</h2>
<p class="center"><img src="images/pyramid-defined.svg" alt="Pyramid Base and Apex" />
<br> A pyramid is made by connecting a <b>base</b> to an <b>apex</b></p>
<p>The base is a <a href="polygons.html">polygon</a> (flat with straight edges) and all other faces are triangles. No curves!</p>
<h2>Types of Pyramids</h2>
<p>There are many types of Pyramids, and they are named after the shape of their base.</p>
<table border="0" align="center">
<tr align="center">
<td class="large">&nbsp; </td>
<td class="large">Pyramid</td>
<td class="large">Base</td>
</tr>
<tr align="center">
<th><a href="triangular-pyramid.html">Triangular
<br /> Pyramid</a>:</th>
<td><img src="images/triangular-pyramid.png" width="152" height="148" alt="Triangular Pyramid" /></td>
<td><img src="images/triangle.svg" alt="Triangle" /></td>
</tr>
<tr align="center">
<th><a href="square-pyramid.html">Square
<br /> Pyramid</a>:</th>
<td><img src="images/square-pyramid.png" width="181" height="130" alt="Square Pyramid" /></td>
<td><img src="images/square.svg" alt="Square" /></td>
</tr>
<tr align="center">
<th><a href="pentagonal-pyramid.html">Pentagonal
<br /> Pyramid</a>:</th>
<td>
<br /> <img src="images/pentagonal-pyramid.png" width="163" height="141" alt="Pentagonal Pyramid" /></td>
<td><img src="images/pentagon.svg" alt="Pentagon" /></td>
</tr>
<tr align="center">
<th colspan="3"><b><i><br />
... and so on ...</i></b></th>
</tr>
</table>
<p>&nbsp;</p>
<p class="center fun"><a href="fly-pyramids.html">Fly through some pyramids here.</a></p>
<h2>Right vs Oblique Pyramid</h2>
<p>This tells us where the top (apex) of the pyramid is. When the apex is directly above the center of the base it is a <b>Right Pyramid</b>, otherwise it is an <b>Oblique Pyramid</b>.</p>
<table border="0" align="center">
<tr>
<td><img src="images/right-pyramid.gif" width="181" height="130" alt="Right Pyramid" /></td>
<td><img src="images/oblique-pyramid.gif" width="181" height="132" alt="Oblique Pyramid" /></td>
</tr>
<tr>
<th>Right Pyramid</th>
<th>Oblique Pyramid</th>
</tr>
</table>
<h2>Regular vs Irregular Pyramid</h2>
<p>This tells us about the <b>shape of the base</b>. When the base is a <a href="regular-polygons.html">regular polygon</a> it is a <b>Regular Pyramid</b>, otherwise it is an <b>Irregular Pyramid</b>.</p>
<table border="0" align="center">
<tr>
<td><img src="images/square-pyramid.png" width="181" height="130" alt="Regular Pyramid" /></td>
<td><img src="images/irregular-pyramid.png" width="129" height="129" alt="Irregular Pyramid" /></td>
</tr>
<tr align="center">
<th>Regular Pyramid</th>
<th>Irregular Pyramid</th>
</tr>
<tr>
<td align="center"><img src="images/square.svg" alt="Square" /></td>
<td><img src="images/irregular-square.gif" width="141" height="106" alt="Irregular Ploygon" /></td>
</tr>
<tr align="center">
<th>Base is Regular</th>
<th>Base is Irregular</th>
</tr>
</table>
<h2>Area and Volume</h2>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/pyramid-height-perimeter.svg" alt="Pyramid Perimeter and Height" /></p>
<h3>The Volume of a Pyramid</h3>
<ul>
<li>
<frac><sup>1</sup>/<sub>3</sub></frac> &times; [Base Area] &times; Height
<br />
<br /> </li>
</ul>
<h3>The Surface Area of a Pyramid</h3>
<p align="left">When all side faces are the same:</p>
<ul>
<li>[Base Area] +
<frac><sup>1</sup>/<sub>2</sub></frac> &times; Perimeter &times; [Slant Length] </li>
</ul>
<p align="left">When side faces are different:</p>
<ul>
<li>[Base Area] + [Lateral Area]</li>
</ul>
<p>&nbsp;</p>
<div class="center80">
<h3>Notes On Surface Area</h3>
<p>The Surface Area has two parts: the area of the base (the <i><b>Base Area</b></i>), and the area of the side faces (the <i><b>Lateral Area</b></i>).</p>
<p> For <i><b>Base Area</b></i> : </p>
<p>It depends on the shape, there are different formulas for triangle, square, etc. See <a href="../area.html">Area</a> for formulas, or our <a href="../area-calculation-tool.html">Area Calculation Tool</a></p>
<p>For <i><b>Lateral Area</b></i> :</p>
<p>When all the side faces are the same:</p>
<ul>
<li>Multiply the perimeter by the &quot;slant length&quot; and divide by 2. This is because the side faces are always triangles and the triangle formula is<i> &quot;base times height divided by 2&quot;</i></li>
</ul>
<p>But when the side faces are different (such as an &quot;irregular&quot; pyramid) we must add up the area of each triangle to find the total lateral area.</p>
</div>
<p>&nbsp;</p>
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<div class="related"> <a href="polyhedron.html">Polyhedron</a> <a href="triangular-pyramid.html">Triangular Pyramid</a> <a href="square-pyramid.html">Square Pyramid</a> <a href="pentagonal-pyramid.html">Pentagonal Pyramid</a> <a href="cylinder.html">Cylinder</a> <a href="cone.html">Cone</a> <a href="pyramid-vs-cone.html">Why is a Pyramid like a Cone?</a> <a href="torus.html">Torus</a> <a href="prisms.html">Prisms</a> <a href="../platonic_solids.html">Platonic Solids</a> </div>
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