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129 lines
6.1 KiB
HTML
129 lines
6.1 KiB
HTML
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<title>Heron's Formula</title>
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<h1 align="center">Heron's Formula</h1>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/triangle-sss.gif" width="150" height="139" alt="triangle sss" /></p>
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<h2>Area of a Triangle from Sides</h2>
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<p>You can calculate the area of a triangle if you know the lengths of all three sides, using a formula that has been known for nearly 2000 years.</p>
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<p>It is called "Heron's Formula" after Hero of Alexandria (see below)</p>
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<p> </p>
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<p>Just use this two step process: </p>
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<p><b>Step 1:</b> Calculate <b>"s"</b> (half of the
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triangles perimeter):</p>
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<p class="center large">s = <span class="intbl"><em>a+b+c</em><strong>2</strong></span><br />
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</p>
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<p><b>Step 2:</b> Then calculate the <b>Area</b>:</p>
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<p class="center"><img src="images/herons-formula.png" width="253" height="33" alt="herons formula A = sqrt( s(s-a)(s-b)(s-c) )" /></p>
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<br />
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<div class="example"><h3>Example: What is the area of a triangle where every side is 5 long?</h3>
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<p>Step 1: s = <span class="intbl"><em>5+5+5</em><strong>2</strong></span> = 7.5<br />
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Step 2: A = √(7.5 × 2.5 × 2.5 × 2.5) = √(117.1875) = <b>10.825...</b></p>
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</div>
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<p>Try it yourself:</p>
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<script type="text/javascript">heronMain();</script>
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<!--<div class="flash">
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<div class="sidebar">
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/hero-of-alexandria.jpg" alt="xAS" width="150" height="180"></p><h3>Hero of Alexandria</h3>
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<p>The formula is credited to Hero (or Heron) of Alexandria, who was a Greek Engineer and Mathematician in 10 – 70 AD.</p>
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<p>Amongst other things, he developed the <b><i>Aeolipile</i></b>, the first known steam engine, but it was treated as a toy!</p>
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</div>
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<h2>Angles</h2>
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<p>In the calculator above I also used the <a href="../algebra/trig-cosine-law.html">Law of Cosines</a> to calculate the angles (for a complete solution). The formula is:</p>
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<p class="center"><img src="images/triangle-angle-from-sides.png" width="210" height="47" alt="triangle angle from sides C = cos^-1( (a^2+b^2-c^2)/2ab )" /></p>
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<p>Where "C" is the angle <b>opposite</b> side "c".</p>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(2352, 2353, 2354, 2355, 3942, 3943, 3944, 3945, 3946, 2356);</script>
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</div>
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<div class="related"><a href="area.html">Area</a>
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<a href="../triangle.html">Triangles</a><a href="index.html">Geometry Index</a></div>
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