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253 lines
9.2 KiB
HTML
253 lines
9.2 KiB
HTML
<!doctype html>
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<html lang="en">
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<!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/area.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:37:17 GMT -->
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<head>
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<meta charset="UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Area of Circle, Triangle, Square, Rectangle, Parallelogram, Trapezium, Ellipse and Sector</title>
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<script language="JavaScript" type="text/javascript">reSpell=[["meter","metre"]];</script>
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<!-- #EndEditable -->
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
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<meta name="HandheldFriendly" content="true">
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<meta name="referrer" content="always">
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<link rel="preload" href="images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin>
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<link rel="preload" href="style4.css" as="style">
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<link rel="preload" href="main4.js" as="script">
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<link rel="stylesheet" href="style4.css">
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<script src="main4.js" defer></script>
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<script>
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window.dataLayer = window.dataLayer || [];
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function gtag(){dataLayer.push(arguments);}
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gtag('js', new Date());
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gtag('config', 'UA-29771508-1');
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</script>
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</head>
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<body id="bodybg">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="adHide"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
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<div id="search" role="search"></div>
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<div id="linkto"></div>
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<div id="menuSlim" class="menu"></div>
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<div id="menuTiny" class="menu"></div>
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</nav>
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<div id="extra"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Area of Plane Shapes</h1>
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<p class="center"><i>Area is the size of a surface!<br>
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Learn more about <a href="geometry/area.html">Area</a>, or try the <a href="area-calculation-tool.html">Area Calculator</a>.</i></p>
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<style>
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.boxa {
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text-align: center;
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display: inline-block;
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vertical-align:bottom;
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border-radius: 17px;
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border: 2px solid hsla(240,100%,70%,10%);
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margin: 0 20px 25px 0;
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width: 320px;
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}
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.imga { background-color:white; float:left; margin: 0px 0px 0px 0px; border-radius: 15px; }
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</style>
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<div class="center">
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<div class="boxa bgb1">
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<div class="imga">
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<a href="triangle.html"><img src="geometry/images/area/triangle2.gif" alt="triangle base height" height="90" width="100" ></a>
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</div>
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<a href="triangle.html">Triangle</a><br>
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<span class="large">Area = ½ × b × h</span><br>
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b = base<br>
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h = vertical height
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</div>
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<div class="boxa bgb1">
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<div class="imga">
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<a href="geometry/square.html"><img src="geometry/images/area/squar2.gif" alt="square" height="90" width="100" ></a>
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</div>
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<a href="geometry/square.html">Square</a><br>
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<span class="large">Area = a<sup>2</sup></span><br>
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a = length of side
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</div>
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<div class="boxa bgb1">
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<div class="imga">
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<a href="geometry/rectangle.html"><img src="geometry/images/area/rectangle.gif" alt="rectangle" height="90" width="100" ></a>
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</div>
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<a href="geometry/rectangle.html">Rectangle</a><br>
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<span class="large">Area = w × h</span><br>
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w = width<br>
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h = height
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</div>
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<div class="boxa bgb1">
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<div class="imga">
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<a href="geometry/parallelogram.html"><img src="geometry/images/area/parallel.gif" alt="parallelogram" height="90" width="100" ></a>
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</div>
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<a href="geometry/parallelogram.html">Parallelogram</a><br>
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<span class="large">Area = b × h</span><br>
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b = base<br>
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h = vertical height
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</div>
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<div class="boxa bgb1">
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<div class="imga">
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<a href="geometry/trapezoid.html"><img src="geometry/images/area/trap.gif" alt="trapezoid" height="90" width="100" ></a>
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</div>
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<a href="geometry/trapezoid.html">Trapezoid (US)</a><br>
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<a href="geometry/trapezoid.html">Trapezium (UK)</a><br>
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<span class="large">Area = ½(a+b) × h</span><br>
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h = vertical height
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</div>
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<div class="boxa bgb1">
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<div class="imga">
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<a href="geometry/circle-area.html"><img src="geometry/images/area/circle.gif" alt="circle" height="90" width="100" ></a>
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</div>
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<a href="geometry/circle-area.html">Circle</a> <br>
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<span class="large">Area = </span><span class="times">π</span><span class="large"> × r<sup>2</sup></span><br>
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r = radius
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</div>
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<div class="boxa bgb1">
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<div class="imga">
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<a href="geometry/ellipse.html"><img src="geometry/images/area/ellipse.gif" alt="ellipse" height="90" width="100" ></a>
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</div>
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<a href="geometry/ellipse.html">Ellipse</a><br>
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<span class="large">Area = </span><span class="times">π</span><span class="large">ab</span><br>
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</div>
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<div class="boxa bgb1">
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<div class="imga">
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<a href="geometry/circle-sector-segment.html"><img src="geometry/images/area/sector.gif" alt="sector" height="90" width="100" ></a>
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</div>
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<a href="geometry/circle-sector-segment.html">Sector</a><br>
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<span class="large">Area = ½ × r<sup>2</sup> × θ </span><br>
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r = radius<br>
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θ = angle in <b>radians</b>
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</div>
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</div>
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<div class="center">
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<img src="geometry/images/altitude.svg" alt="altitude" height="75" width="113" ><br>
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Note: <b>h</b> is at <a href="rightangle.html">right angles</a> to <b>b</b>
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</div>
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<p> </p>
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<div class="example">
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<h3>Example: What is the area of this rectangle?</h3>
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<p class="center"><img src="geometry/images/area-rectangle.svg" alt="Area Rectangle" height="111" width="163" ></p>
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<p>The formula is:</p>
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<p class="center"><span class="larger">Area = w × h</span><br>
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w = width<br>
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h = height</p>
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<p>We know <b>w = 5</b> and <b>h = 3</b>, so:</p>
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<p class="center larger">Area = 5 × 3 = <b>15</b></p>
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</div>
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<div class="example">
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<h3>Example: What is the area of this circle?</h3>
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<p class="center"><img src="geometry/images/circle-area-ex.svg" alt="circle radius 3" height="119" width="119" ></p>
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<p class="center">Radius = r = 3</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:right;"><span class="larger">Area</span></td>
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<td> </td>
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<td><span class="larger">= <span class="times">π</span> × r<sup>2</sup></span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td><span class="larger">= <span class="times">π</span> × 3<sup>2</sup></span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td><span class="larger">= <span class="times">π</span> × (3 × 3)</span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td><span class="larger">= 3.14159... × 9</span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td><span class="larger">= <b>28.27</b> (to 2 decimal places)</span></td>
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</tr>
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</tbody></table>
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</div>
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<div class="example">
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<h3>Example: What is the area of this triangle?</h3>
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<p class="center"><img src="geometry/images/triangle-area-example.svg" alt="Triangle base=20, height=12" height="135" width="217" ></p>
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<p class="center">Height = h = 12</p>
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<p class="center">Base = b = 20</p>
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<p class="center larger">Area = ½ × b × h = ½ × 20 × 12 = <b>120</b></p>
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</div>
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<p> </p>
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<p>A harder example:</p>
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<div class="example">
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<h3>Example: Sam cuts grass at $0.10 per square meter</h3>
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<h3>How much does Sam earn cutting this area:</h3>
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<p class="center"><img src="geometry/images/area-grass.svg" alt="area grass" height="118" width="205" ></p>
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<p>Let's break the area into two parts:</p>
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<p class="center"><img src="geometry/images/area-grass2.svg" alt="area grass in parts" height="118" width="205" ></p>
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<p>Part A is a square:</p>
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<div class="so">Area of A = a<sup>2</sup> = 20m × 20m = 400m<sup>2</sup></div>
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<p>Part B is a triangle. Viewed sideways it has a base of 20m and a height of 14m.</p>
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<div class="so">Area of B = ½b × h = ½ × 20m × 14m = 140m<sup>2</sup></div>
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<p>So the total area is:</p>
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<div class="so">Area = Area of A + Area of B = 400m<sup>2</sup> + 140m<sup>2</sup> = 540m<sup>2</sup></div>
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<p> </p>
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<p>Sam earns $0.10 per square meter</p>
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<div class="so">Sam earns = $0.10 × 540m<sup>2</sup> = $54</div>
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</div>
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<p> </p>
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<div class="questions">1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 3250, 3251</div>
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<div class="related">
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<a href="area-calculation-tool.html">Area Calculation Tool</a>
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<a href="geometry/area.html">Area</a>
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<a href="geometry/area-irregular-polygons.html">Area of Irregular Polygons</a>
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<a href="geometry/index.html">Geometry Index</a>
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</div>
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<!-- #EndEditable -->
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</article>
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<div id="adend" class="centerfull noprint"></div>
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<footer id="footer" class="centerfull noprint"></footer>
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<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
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</div>
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</body>
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<!-- #EndTemplate -->
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<!-- Mirrored from www.mathsisfun.com/area.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:37:20 GMT -->
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