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217 lines
7.8 KiB
HTML
217 lines
7.8 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/geometry/trapezoid.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:38:45 GMT -->
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<title>Trapezoid</title>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Trapezoid</h1>
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<p class="center"><i>(Jump to <a href="#Area">Area of a Trapezoid</a> or <a href="#Perimeter">Perimeter of a Trapezoid</a>)</i></p>
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<p>A trapezoid is a 4-sided flat shape with straight sides that has <b>a pair of opposite sides parallel</b> (marked with arrows below):</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td style="text-align:center;"><img src="images/trapez.svg" alt="trapezoid" height="122" width="204"></td>
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<td style="text-align:center; width:20px;"> </td>
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<td style="text-align:center;"><img src="images/trapez-isosceles.svg" alt="Isosceles trapezoid" height="122" width="204"></td>
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</tr>
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<tr>
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<td class="larger" align="center">Trapezoid</td>
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<td style="text-align:center;"> </td>
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<td class="larger" align="center">Isosceles Trapezoid</td>
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</tr>
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</tbody></table>
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<p>A trapezoid:</p>
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<table cellpadding="5" border="0">
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<tbody>
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<tr>
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<td><img src="../images/style/right-arrow.gif" alt="right arrow" height="46" width="46"></td>
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<td>has a pair of <a href="../perpendicular-parallel.html">parallel</a> sides</td>
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</tr>
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<tr>
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<td><img src="../images/style/right-arrow.gif" alt="right arrow" height="46" width="46"></td>
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<td>
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<p>is an <b>isosceles</b> trapezoid when it has <b>equal angles</b> from a parallel side</p></td>
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</tr>
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<tr>
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<td><img src="../images/style/right-arrow.gif" alt="right arrow" height="46" width="46"></td>
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<td>is called a "<b>trapezium</b>" in the UK (see <a href="#lang">below</a>)</td>
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</tr>
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</tbody></table>
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<p>Play with a trapezoid:</p>
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<div class="script" style="height: 330px;">
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images/geom-quad.js?mode=trapezoid
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</div>
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<p> </p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/trapez-base-leg.svg" alt="trapezoid base leg and altitude" height="149" width="200"></p>
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<p>The parallel sides are the "bases"</p>
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<p>The other two sides are the "legs"</p>
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<p>The distance (at right angles) from one base to the other is called the "altitude"</p>
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<h2><a name="Area"></a>Area
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of a Trapezoid</h2>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td><img src="images/trapez-area.svg" alt="trapezoid a, b, h" height="" width=""></td>
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<td> </td>
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<td>
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<p>The Area is the <b>average of the two base lengths</b> times the <b>altitude</b>:</p>
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<p class="center large">Area = <span class="intbl"><em>a+b</em><strong>2</strong></span> × h</p></td>
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</tr>
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</tbody></table>
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<div class="example">
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<h3>Example: A <span class="center">trapezoid</span>'s two bases are 6 m and 4m, and it is 3m high. What is its Area?</h3>
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<p>Area = <span class="intbl"><em>6 m + 4 m</em><strong>2</strong></span> × 3 m = 5 m × 3 m = <b>15 m<sup>2</sup></b></p>
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</div>
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<p>The <span class="center"><a href="area-polygon-drawing.html">Area of Polygon by Drawing</a></span> tool is helpful when you can draw your Trapezoid.</p>
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<h2><a name="Perimeter"></a>Perimeter of a Trapezoid</h2>
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<p>The Perimeter is the distance around the edges.</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td><img src="images/trapez-perim.svg" alt="trapezoid perimeter a+b+c+d" height="" width=""></td>
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<td> </td>
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<td>
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<p>The Perimeter is <b>the sum of all side lengths</b>:</p>
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<p class="center larger">Perimeter = a+b+c+d</p></td>
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</tr>
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</tbody></table>
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<div class="example">
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<h3>Example: A trapezoid has side lengths of 5 cm, 12 cm, 4 cm and 15 cm, what is its Perimeter?</h3>
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<p>Perimeter = 5 cm + 12 cm + 4 cm + 15 cm = <b>36 cm</b></p>
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</div>
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<h2>Median of a Trapezoid</h2>
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<table width="100%" border="0">
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<tbody>
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<tr>
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<td><img src="images/trapez-median.svg" alt="trapezoid median half-way between a and b" height="" width=""></td>
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<td> </td>
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<td>
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<p>The <b>median</b> (also called a midline or midsegment) is a line segment half-way between the two bases.</p>
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<p>The median's length is the average of the two base lengths:</p>
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<p class="center large">m = <span class="intbl"><em>a+b</em><strong>2</strong></span></p></td>
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</tr>
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</tbody></table>
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<p>You can calculate the area when you know the median, it is just the median times the height:</p>
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<p class="center larger">Area = mh</p>
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<h2>Trapezium</h2>
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<a id="lang"></a>
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<p>A <b>trapezium</b> (UK: trapezoid) is a quadrilateral with NO parallel sides.</p>
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<p>The US and UK have their definitions swapped over, like this:</p>
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<table align="center" cellpadding="5" border="0">
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<tbody>
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<tr>
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<td style="text-align:center;"> </td>
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<td style="text-align:center;">Trapezoid</td>
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<td style="text-align:center;">Trapezium</td>
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</tr>
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<tr>
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<td style="text-align:center;">US:</td>
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<td class="bga1" align="center">a pair of parallel sides</td>
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<td class="bgb1" align="center">NO parallel sides</td>
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</tr>
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<tr>
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<td style="text-align:center;">UK:</td>
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<td class="bgb1" align="center">NO parallel sides</td>
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<td class="bga1" align="center">a pair of parallel sides</td>
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</tr>
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</tbody></table>
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<p> </p>
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<div class="questions">9131, 9132, 9133, 9134, 9135, 9136, 9137, 9138, 9139, 9140</div>
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<div class="related">
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<a href="../quadrilaterals.html">Quadrilaterals</a>
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<a href="index.html">Geometry Index</a>
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</div>
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<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
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