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288 lines
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HTML
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<title>Prisms with Examples</title>
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Prisms</h1>
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<p class="center"><i>Go to <a href="#Area">Surface Area</a> or <a href="#Volume">Volume</a>.</i></p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/poly-pent-prism.svg" alt="pentagonal prism" width="200"></p>
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<p class="larger">A prism is a solid object with:</p>
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<div class="bigul">
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<ul>
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<li>identical ends</li>
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<li>flat faces</li>
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<li>and the same <b><a href="cross-sections.html">cross section</a></b> all along its length !</li>
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</ul>
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</div>
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<p> </p>
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<p>A <b>cross section</b> is the shape made by cutting straight across an object.</p>
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<p style="float:left; margin: 0 20px 5px 0;"><img src="images/prism-cross-section.jpg" alt="prism cross section" height="186" width="173"></p>
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<p>The cross section of this object is a <b>triangle</b> ...</p>
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<p>.. it has the same cross section all along its length ...</p>
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<p>... so it's a <b>triangular prism.</b></p>
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<div class="script">
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images/prism-grow.js
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</div>
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<table style="border: 0;">
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<tbody>
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<tr>
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<td style="text-align:right;">
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<p class="large">
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Try drawing a <b>shape</b> on a piece of<br>
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paper (using straight lines)</p>
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<p class="large">Then imagine it extending up from the sheet of paper ...<br>
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... that's a prism !</p>
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</td>
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<td><img src="images/prism-draw.gif" alt="Drawing a Prism" height="147" width="172"></td>
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</tr>
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</tbody></table>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/prism-not-cylinder.jpg" alt="Prism not cylinder" height="202" width="138"></p>
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<h2>No Curves!</h2>
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<p>A prism is a <a href="polyhedron.html">polyhedron</a>, which means all faces are flat!</p>
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<div class="center80">
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<p class="center larger">No curved sides.</p>
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</div>
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<p>For example, <b>a <a href="cylinder.html">cylinder</a> is not a prism</b>, because it has curved sides.</p>
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<h2>Bases</h2>
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<p class="center"><img src="images/bases.svg" alt="bases"><br>
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The ends of a prism are parallel<br>
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and each one is called a base.</p>
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<h2>Sides</h2>
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<p class="center"><img src="images/prism-sides-small.svg" alt="prism sides parallel"><br>
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The side faces of a prism are <a href="parallelogram.html">parallelograms</a><br>
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(4-sided shapes with opposite sides parallel)</p>
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<h2>These are all Prisms:</h2>
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<div class="clear">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td class="large" colspan="2">
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<hr> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">Square Prism:</td>
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<td class="large">Cross-Section:</td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="images/cuboid.svg" alt="cuboid"></td>
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<td><img src="images/square.svg" alt="square"></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="2" class="large">
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<hr> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">Cube:</td>
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<td class="large">Cross-Section:</td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="images/cube.svg" alt="cube"></td>
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<td><img src="images/square.svg" alt="square"></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="2">(yes, a cube is a prism, because it is a square<br>
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all along its length)<br>
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(Also see <a href="cuboids-rectangular-prisms.html">Rectangular Prisms</a> ) </td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="2">
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<hr> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">Triangular Prism:</td>
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<td class="large">Cross-Section:</td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="images/tri-prism.svg" alt="triangular prism"></td>
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<td><img src="images/triangle.svg" alt="triangle"></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="2" class="large">
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<hr> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">Pentagonal Prism:</td>
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<td class="large">Cross-Section:</td>
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</tr>
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<tr style="text-align:center;">
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<td><br>
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<img src="images/poly-pent-prism.svg" alt="pentagonal prism" width="175"></td>
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<td><img src="images/pentagon.svg" alt="pentagon"></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="2">
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<hr></td>
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</tr>
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</tbody></table>
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</div>
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<p class="center">and more!</p>
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<div class="example">
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/snowflake2.jpg" alt="Hexagonal Ice Crystal" width="175"></p>
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<h3>Example: This hexagonal ice crystal.</h3>
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<p><br>
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It looks like a hexagon, but because it has some thickness it is actually a hexagonal prism!</p>
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<p> </p>
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<p><i>Photograph by NASA / Alexey Kljatov.</i></p>
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</div>
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<h2>Regular vs Irregular Prisms</h2>
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<p>All the previous examples are <b>Regular</b> Prisms, because the cross section is regular (in other words it is a shape with equal edge lengths, and equal angles.)</p>
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<p>Here is an example of an <b>Irregular Prism</b>:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td class="large" height="22">Irregular Pentagonal Prism:</td>
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<td class="large"> </td>
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<td class="large" height="22"> </td>
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</tr>
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<tr style="text-align:center;">
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<td rowspan="2"><br>
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<img src="images/irr-pentagonal-prism.png" alt="irregular pentagonal prism" height="119" width="181"></td>
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<td> </td>
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<td><img src="images/irregular-pentagon.png" alt="irregular pentagon" height="110" width="141"></td>
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</tr>
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<tr style="text-align:center;">
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<td> </td>
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<td>Cross-Section</td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3">It is "irregular" because the<br>
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cross-section is not "regular" in shape.</td>
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</tr>
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</tbody></table>
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<a id="Area"></a>
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<h2>Right vs Oblique Prism</h2>
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<p>When the two ends are perfectly aligned it is a Right Prism otherwise it is an Oblique Prism:</p>
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<p class="center"><img src="images/prism-oblique.svg" alt="right vs oblique prism"></p>
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<h2>Surface Area of a Prism</h2>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/prism-area-perimeter.svg" alt="prism area of base, perimeter of base and length"></p>
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<p> </p>
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<div class="tbl">
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<div class="row"><span class="left">Surface Area = </span><span class="right"><span class="large">2 × Base Area<br>
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+ Base Perimeter × Length </span></span></div>
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</div>
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<div style="clear:both"></div>
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<div class="example">
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<h3>Example: What is the surface area of a prism where the base area is 25 m<sup>2</sup>, the base perimeter is 24 m, and the length is 12 m:</h3>
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<p> </p>
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<div class="tbl">
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<div class="row"><span class="left">Surface Area </span><span class="right">= 2 × Base Area + Base Perimeter × Length</span></div>
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<div class="row"><span class="left"> </span><span class="right">= 2 × 25 <span class="center"> m<sup>2</sup></span> + 24 m × 12 m</span></div>
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<div class="row"><span class="left"> </span><span class="right">= 50 <span class="center"> m<sup>2</sup></span> + 288 <span class="center"> m<sup>2</sup></span></span></div>
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<div class="row"><span class="left"> </span><span class="right"><span class="center">= <b>338 m<sup>2</sup></b></span></span></div>
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</div>
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<p> </p>
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<p>(Note: we have an <a href="../area-calculation-tool.html">Area Calculation Tool</a>)</p>
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</div>
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<a id="Volume"></a>
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<h2>Volume of a Prism</h2>
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<p>The Volume of a prism is the area of one end times the length of the prism.</p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/prism-area-perimeter.svg" alt="prism area of base, perimeter of base and length"></p>
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<p class="large center">Volume = Base Area × Length</p>
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<div class="example">
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<h3>Example: What is the volume of a prism where the base area is 25 m<sup>2</sup> and which is 12 m long:<br>
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</h3>
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<div class="tbl">
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<div class="row"><span class="left">Volume </span><span class="right">= Area × Length</span></div>
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<div class="row"><span class="left"> </span><span class="right">= 25 m<sup>2</sup> × 12 m</span></div>
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<div class="row"><span class="left"> </span><span class="right">= <b>300 m<sup>3</sup></b></span></div>
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</div>
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</div>
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<p>Play with it here. The formula also works when it "leans over" (<i>oblique</i>) but remember that the height is at right angles to the base:</p>
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<iframe src="isquare-prism.html" scrolling="no" style="width:362px; height:302px; overflow:hidden; margin:auto; display:block; border: none; text-align:center;"></iframe> <div style="clear:both"></div>
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<p>And this is why:</p>
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<p class="center"><img src="images/prism-stack-right.jpg" alt="cards stacked right" height="182" width="188"> <img src="images/prism-stack-oblique.jpg" alt="cards stacked right" height="180" width="241"><br>
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The stack can lean over, but still has the same volume</p>
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<h2> </h2>
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<h2>More About The Side Faces</h2>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/prism-sides.svg" alt="prism sides"></p>
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<p>The side faces of a prism are <a href="parallelogram.html">parallelograms</a> (<span class="center">4-sided shape with opposites sides parallel</span>)</p>
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<p> </p>
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<p>A prism can lean to one side, making it an <b>oblique prism</b>, but the two ends are still parallel, and the side faces are still parallelograms!</p>
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<p> </p>
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<p>But if the two ends are <b>not parallel</b> it is <b>not a prism</b>.</p>
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<div style="clear:both"></div>
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<p> </p>
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<div class="questions">639,640,863, 1826, 1827,864, 3379, 3377, 3378, 7649</div>
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<div class="related">
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<a href="prism-vs-cylinder.html">Prism vs Cylinder</a>
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<a href="polyhedron.html">Polyhedron</a>
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<a href="cuboids-rectangular-prisms.html">Cuboids / Rectangular Prisms</a>
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<a href="../platonic_solids.html">Platonic Solids</a>
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<a href="cylinder.html">Cylinder</a>
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<a href="cone.html">Cone</a>
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<a href="sphere.html">Sphere</a>
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<a href="torus.html">Torus</a>
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</div>
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<!-- #EndEditable -->
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</article>
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<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
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