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<!doctype html> <html lang="en" class="geometry interactiveentries"> <head> <title>Kite -- from Wolfram MathWorld</title> <meta name="DC.Title" content="Kite" /> <meta name="DC.Creator" content="Weisstein, Eric W." /> <meta name="DC.Description" content="A kite is a planar convex quadrilateral consisting of two adjacent sides of length a and the other two sides of length b. The rhombus is a special case of the kite, and the lozenge is a special case of the rhombus. The area of a kite is given by A=1/2pq, (1) where p = sqrt(a^2-h^2)+sqrt(b^2-h^2) (2) q = 2h (3) are the lengths of the polygon diagonals (which are perpendicular). The 120-90-60-90 kite with edge ratios sqrt(3):1 is the basis for the polyomino-like objects known as..." /> <meta name="description" content="A kite is a planar convex quadrilateral consisting of two adjacent sides of length a and the other two sides of length b. The rhombus is a special case of the kite, and the lozenge is a special case of the rhombus. The area of a kite is given by A=1/2pq, (1) where p = sqrt(a^2-h^2)+sqrt(b^2-h^2) (2) q = 2h (3) are the lengths of the polygon diagonals (which are perpendicular). The 120-90-60-90 kite with edge ratios sqrt(3):1 is the basis for the polyomino-like objects known as..." /> <meta name="DC.Date.Modified" scheme="W3CDTF" content="2003-10-06" /> <meta name="DC.Date.Modified" scheme="W3CDTF" content="2010-08-11" /> <meta name="DC.Date.Modified" scheme="W3CDTF" content="2024-04-25" /> <meta name="DC.Subject" scheme="MathWorld" content="Mathematics:Geometry:Plane Geometry:Quadrilaterals" /> <meta name="DC.Subject" scheme="MathWorld" content="Mathematics:Geometry:Plane Geometry:Tiling" /> <meta name="DC.Subject" scheme="MathWorld" content="Mathematics:Interactive Entries:Click to Copy" /> <meta name="DC.Subject" scheme="MSC_2000" content="05B45" /> <meta name="DC.Subject" scheme="MSC_2000" content="51M04" /> <meta name="DC.Rights" content="Copyright 1999-2024 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement." /> <meta name="DC.Format" scheme="IMT" content="text/html" /> <meta name="DC.Identifier" scheme="URI" content="https://mathworld.wolfram.com/Kite.html" /> <meta name="DC.Language" scheme="RFC3066" content="en" /> <meta name="DC.Publisher" content="Wolfram Research, Inc." /> <meta name="DC.Relation.IsPartOf" scheme="URI" content="https://mathworld.wolfram.com/" /> <meta name="DC.Type" scheme="DCMIType" content="Text" /> <meta name="Last-Modified" content="2024-04-25" /> <meta property="og:image" content="https://mathworld.wolfram.com/images/socialmedia/share/ogimage_Kite.png"> <meta property="og:url" content="https://mathworld.wolfram.com/Kite.html"> <meta property="og:type" content="website"> <meta property="og:title" content="Kite -- from Wolfram MathWorld"> <meta property="og:description" content="A kite is a planar convex quadrilateral consisting of two adjacent sides of length a and the other two sides of length b. The rhombus is a special case of the kite, and the lozenge is a special case of the rhombus. The area of a kite is given by A=1/2pq, (1) where p = sqrt(a^2-h^2)+sqrt(b^2-h^2) (2) q = 2h (3) are the lengths of the polygon diagonals (which are perpendicular). The 120-90-60-90 kite with edge ratios sqrt(3):1 is the basis for the polyomino-like objects known as..."> <meta name="twitter:card" content="summary_large_image"> <meta name="twitter:site" content="@WolframResearch"> <meta name="twitter:title" content="Kite -- from Wolfram MathWorld"> <meta name="twitter:description" content="A kite is a planar convex quadrilateral consisting of two adjacent sides of length a and the other two sides of length b. The rhombus is a special case of the kite, and the lozenge is a special case of the rhombus. The area of a kite is given by A=1/2pq, (1) where p = sqrt(a^2-h^2)+sqrt(b^2-h^2) (2) q = 2h (3) are the lengths of the polygon diagonals (which are perpendicular). The 120-90-60-90 kite with edge ratios sqrt(3):1 is the basis for the polyomino-like objects known as..."> <meta name="twitter:image:src" content="https://mathworld.wolfram.com/images/socialmedia/share/ogimage_Kite.png"> <link rel="canonical" href="https://mathworld.wolfram.com/Kite.html" /> <meta http-equiv="x-ua-compatible" content="ie=edge"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta charset="utf-8"> <script async src="/common/javascript/analytics.js"></script> <script async src="//www.wolframcdn.com/consent/cookie-consent.js"></script> <script async src="/common/javascript/wal/latest/walLoad.js"></script> <link rel="stylesheet" href="/css/styles.css"> <link rel="preload" href="//www.wolframcdn.com/fonts/source-sans-pro/1.0/global.css" as="style" onload="this.onload=null;this.rel='stylesheet'"> <noscript><link rel="stylesheet" href="//www.wolframcdn.com/fonts/source-sans-pro/1.0/global.css"></noscript> </head> <body id="topics"> <main id="entry"> <div 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History and Terminology </a> <a href="/topics/NumberTheory.html" id="sidebar-numbertheory"> Number Theory </a> <a href="/topics/ProbabilityandStatistics.html" id="sidebar-probabilityandstatistics"> Probability and Statistics </a> <a href="/topics/RecreationalMathematics.html" id="sidebar-recreationalmathematics"> Recreational Mathematics </a> <a href="/topics/Topology.html" id="sidebar-topology"> Topology </a> </nav> <nav class="secondary-nav"> <a href="/letters/"> Alphabetical Index </a> <a href="/whatsnew/"> New in MathWorld </a> </nav> </section> <section id="content">  <nav class="breadcrumbs"><ul class="breadcrumb"> <li> <a href="/topics/Geometry.html">Geometry</a> </li> <li> <a href="/topics/PlaneGeometry.html">Plane Geometry</a> </li> <li> <a href="/topics/Quadrilaterals.html">Quadrilaterals</a> </li> </ul><ul class="breadcrumb"> <li> <a href="/topics/Geometry.html">Geometry</a> </li> <li> <a href="/topics/PlaneGeometry.html">Plane Geometry</a> </li> <li> <a href="/topics/Tiling.html">Tiling</a> </li> </ul><ul class="breadcrumb"> <li> <a href="/topics/InteractiveEntries.html">Interactive Entries</a> </li> <li> <a href="/topics/ClicktoCopy.html">Click to Copy</a> </li> </ul></nav>   <h1>Kite</h1>  <hr class="margin-t-1-8 margin-b-3-4">  <div class="attachments text-align-r"> <a href="/notebooks/PlaneGeometry/Kite.nb" download="Kite.nb"><img src="/images/entries/download-notebook-icon.png" width="26" height="27" alt="DOWNLOAD Mathematica Notebook" /><span>Download <span class="display-i display-n__600">Wolfram </span>Notebook</span></a> </div>  <div class="entry-content"> <div class="center-image"> <img style="max-width:100%;max-height:100%;" width="509.82" height="108.809" src="images/eps-svg/Kite_751.svg" class="" alt="Kite" /> </div> <p> A kite is a planar convex <a href="/Quadrilateral.html">quadrilateral</a> consisting of two adjacent sides of length <img src="/images/equations/Kite/Inline1.svg" class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="9" height="21" alt="a" /> and the other two sides of length <img src="/images/equations/Kite/Inline2.svg" class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="9" height="21" alt="b" />. The <a href="/Rhombus.html">rhombus</a> is a special case of the kite, and the <a href="/Lozenge.html">lozenge</a> is a special case of the <a href="/Rhombus.html">rhombus</a>. </p> <p> The <a href="/Area.html">area</a> of a kite is given by </p> <div> <table summary="" width="100%" align="center" cellspacing="0" cellpadding="0" style="padding-left: 50px"> <tr><td align="left"><img src="/images/equations/Kite/NumberedEquation1.svg" class="numberedequation" style="max-height:100%;max-width:100%" border="0" width="73" height="26" alt=" A=1/2pq, " /></td><td align="right" width="3"> <div id="eqn1" class="eqnum"> (1) </div> </td></tr> </table> </div> <p> where </p> <div class="table-responsive-noborders"> <table align="center" width="100%" cellpadding="0" cellspacing="0" style="padding-left: 50px" border="0"> <tr style=""><td align="right" width=""><img src="/images/equations/Kite/Inline3.svg" class="displayformula" style="max-height:100%;max-width:100%" border="0" width="10" height="20" alt="p" /></td><td align="center" width="14"><img src="/images/equations/Kite/Inline4.svg" class="displayformula" style="max-height:100%;max-width:100%" border="0" width="10" height="20" alt="=" /></td><td align="left"><img src="/images/equations/Kite/Inline5.svg" class="displayformula" style="max-height:100%;max-width:100%" border="0" width="149" height="24" alt="sqrt(a^2-h^2)+sqrt(b^2-h^2)" /></td><td align="right" width="10"> <div id="eqn2" class="eqnum"> (2) </div> </td></tr><tr style=""><td align="right" width=""><img src="/images/equations/Kite/Inline6.svg" class="displayformula" style="max-height:100%;max-width:100%" border="0" width="9" height="20" alt="q" /></td><td align="center" width="14"><img src="/images/equations/Kite/Inline7.svg" class="displayformula" style="max-height:100%;max-width:100%" border="0" width="10" height="20" alt="=" /></td><td align="left"><img src="/images/equations/Kite/Inline8.svg" class="displayformula" style="max-height:100%;max-width:100%" border="0" width="21" height="20" alt="2h" /></td><td align="right" width="10"> <div id="eqn3" class="eqnum"> (3) </div> </td></tr> </table> </div> <p> are the lengths of the <a href="/PolygonDiagonal.html">polygon diagonals</a> (which are <a href="/Perpendicular.html">perpendicular</a>). </p> <p> The 120-90-60-90 kite with edge ratios <img src="/images/equations/Kite/Inline9.svg" class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="51" height="23" alt="sqrt(3):1" /> is the basis for the <a href="/Polyomino.html">polyomino</a>-like objects known as <a href="/Polykite.html">polykites</a>. </p> <div class="center-image"> <img style="max-width:100%;max-height:100%;" width="237.75" height="279.594" src="images/eps-svg/KitePenroseTile_600.svg" class=" wolfram-c2c-wrapper mathworld-c2c_above" alt="KitePenroseTile" data-c2c-file="/mathcode/KitePenroseTile.txt" data-c2c-type="text/html" /> </div> <p> "Kite" is also the name given to the <a href="/PenroseTiles.html">Penrose tile</a> illustrated above. </p> </div>  <hr class="margin-b-1-1-4"> <div class="c-777 entry-secondary-content">  <h2>See also</h2><a href="/Dart.html">Dart</a>, <a href="/KiteGraph.html">Kite Graph</a>, <a href="/KrackhardtKite.html">Krackhardt Kite</a>, <a href="/Lozenge.html">Lozenge</a>, <a href="/Parallelogram.html">Parallelogram</a>, <a href="/PenroseTiles.html">Penrose Tiles</a>, <a href="/Polykite.html">Polykite</a>, <a href="/Quadrilateral.html">Quadrilateral</a>, <a href="/Rhombus.html">Rhombus</a>       <h2>Explore with Wolfram|Alpha</h2> <div id="WAwidget"> <div class="WAwidget-wrapper"> <img alt="WolframAlpha" title="WolframAlpha" src="/images/wolframalpha/WA-logo.png" width="136" height="20"> <form name="wolframalpha" action="https://www.wolframalpha.com/input/" target="_blank"> <input type="text" name="i" class="search" placeholder="Solve your math problems and get step-by-step solutions" value=""> <button type="submit" title="Evaluate on WolframAlpha"></button> </form> </div> <div class="WAwidget-wrapper try"> <p class="text-align-r"> More things to try: </p> <ul> <li> <a target="_blank" href="http://www.wolframalpha.com/entities/geometry/kite/kp/vr/kr/"> kite </a> </li> <li><a target="_blank" href="https://www.wolframalpha.com/input/?i=annulus%2C+inner+radius%3D2%2C+outer+radius%3D5">annulus, inner radius=2, outer radius=5</a></li> <li><a target="_blank" href="https://www.wolframalpha.com/input/?i=cubic+fit+20.9%2C23.2%2C26.2%2C26.4%2C16.3%2C-12.2%2C-60.6%2C-128.9">cubic fit 20.9,23.2,26.2,26.4,16.3,-12.2,-60.6,-128.9</a></li> </ul> </div> </div>   <h2>References</h2><cite>Harris, J. W. and Stocker, H. "Kite." §3.6.9 in <i><a href="http://www.amazon.com/exec/obidos/ASIN/0387947469/ref=nosim/ericstreasuretro">Handbook of Mathematics and Computational Science.</a></i> New York: Springer-Verlag, p. 86, 1998.</cite>   <h2>Cite this as:</h2> <p> <a href="/about/author.html">Weisstein, Eric W.</a> "Kite." 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