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<!DOCTYPE html>
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
<!-- Mirrored from www.mathsisfun.com/geometry/triangular-pyramid.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:27 GMT -->
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<title>Spinning Triangular Pyramid</title>
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<h1 class="center">Triangular Pyramid</h1>
<p class="center"><i>Go to <a href="#Area">Surface Area</a> or <a href="#Volume">Volume</a>.</i></p>
<div class="centerfull">
<div class="boxa">
<div class="head">Triangular Pyramid Facts</div>
<p><b>Notice these interesting things:</b></p>
<ul>
<li>It has 4 Faces</li>
<li>The 3 Side Faces are Triangles</li>
<li>The Base is also a Triangle</li>
<li>It has 4 Vertices (corner points)</li>
<li>It has 6 Edges</li>
<li>It is also a <a href="tetrahedron.html">Tetrahedron</a></li>
</ul>
</div>
<div class="boxb">
<div class="script" style="height: 450px;">
images/polyhedra.js?mode=tetrahedron
</div>
</div>
</div>
<div style="clear:both"></div>
<a id="Area"></a>
<h2>Surface Area</h2>
<p class="center"><img src="images/triangular-pyramid-height.svg" alt="triangular pyramid height, side length and perimeter" height="229" width="261"></p>
<p><span class="center">When side faces are the same</span>:</p>
<p class="center"><b>Surface Area</b> = [Base Area] + <span class="intbl">
<em>1</em>
<strong>2</strong>
</span> × Perimeter × [Slant Length]</p>
<div class="example">
<h3>Example: <span class="center">Base Area is 28, Perimeter is 20, Slant length is 5</span></h3>
<div class="tbl">
<div class="row"><span class="left"><span class="center">Surface Area </span></span><span class="right">= [Base Area] + <span class="intbl">
<em>1</em>
<strong>2</strong>
</span> × Perimeter × [<span class="center">Slant</span> Length]</span></div>
<div class="row"><span class="left">&nbsp;</span><span class="rtlt">= 28 + <span class="intbl">
<em>1</em>
<strong>2</strong>
</span> × 20 × 5</span></div>
<div class="row"><span class="left">&nbsp;</span><span class="rtlt">= 28 + 50</span></div>
<div class="row"><span class="left">&nbsp;</span><span class="rtlt">= 78</span></div>
</div>
</div>
<p>When side faces are different we can calculate the area of the base and each triangular face separately and then add them up.</p>
<a id="Volume"></a>
<h2>Volume</h2>
<p class="center"><b>Volume</b> = <span class="intbl">
<em>1</em>
<strong>3</strong>
</span> × [Base Area] × Height</p>
<div class="example">
<h3>Example: base area is 28, height is 4.5</h3>
<div class="tbl">
<div class="row"><span class="left"><span class="center">Volume</span></span><span class="right">= <span class="intbl">
<em>1</em>
<strong>3</strong>
</span> × [Base Area] × Height</span></div>
<div class="row"><span class="left">&nbsp;</span><span class="rtlt">= <span class="intbl">
<em>1</em>
<strong>3</strong>
</span> × 28 × 4.5</span></div>
<div class="row"><span class="left">&nbsp;</span><span class="rtlt">= <span class="intbl">
<em>1</em>
<strong>3</strong>
</span> × 126</span></div>
<div class="row"><span class="left">&nbsp;</span><span class="rtlt">= 42</span></div>
</div>
</div>
<p class="center"><img src="images/tetrahedron.svg" alt="triangular pyramid" height="" width=""></p>
<p>&nbsp;</p>
<div class="related">
<a href="tetrahedron.html">Tetrahedron</a>
<a href="pyramids.html">Pyramids</a>
<a href="square-pyramid.html">Square Pyramid</a>
<a href="pyramid-vs-cone.html">Why is a Pyramid like a Cone?</a>
<a href="solid-geometry.html">Solid Geometry</a>
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