<p><b>十五邊形（英語：<span lang="en">Pentadecagon、Pentakaidecagon 或 15-gon</span>）</b>，是幾何學上任何擁有15條邊和15隻角的多邊形。
</p><p>正十五邊形的內角是156°或<span><span><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{15}}}">
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    <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{15}}}</annotation>
  </semantics></math></span></span>弧度
</p><p>正十五邊形的面積公式：
</p><p><span><span><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}A&amp;={\frac {15}{4}}a^{2}\cot {\frac {\pi }{15}}\\&amp;={\frac {15a^{2}}{8}}\left({\sqrt {3}}+{\sqrt {15}}+{\sqrt {10+2{\sqrt {5}}}}\right)\\&amp;\approx 17.6424\,a^{2}.\end{aligned}}}">
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                <mi>A</mi>
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                <mi></mi>
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                    <mn>15</mn>
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                      <mn>15</mn>
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                    <mn>8</mn>
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                  <mo>(</mo>
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                        <mn>10</mn>
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                            <mn>5</mn>
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</p><p>其中<span><span><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">
  <semantics>
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  </semantics></math></span></span>表示面積，<span><span><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}">
  <semantics>
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</p>
<h2><span id=".E5.B0.BA.E8.A6.8F.E4.BD.9C.E5.9C.96"></span><span id="尺規作圖">尺規作圖</span></h2>
<p>有一個尺規作圖的方法可以畫出準確的正十五邊形，方法如右圖所示，總計有36步。

</p>
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**十五邊形（英語：Pentadecagon、Pentakaidecagon 或 15-gon）** ，是幾何學上任何擁有 15 條邊和 15 隻角的多邊形。

正十五邊形的內角是 156° 或 ${\frac {\pi }{15}}$ 弧度

正十五邊形的面積公式：

$$
{\begin{aligned}A&={\frac {15}{4}}a^{2}\cot {\frac {\pi }{15}}\\&={\frac {15a^{2}}{8}}\left({\sqrt {3}}+{\sqrt {15}}+{\sqrt {10+2{\sqrt {5}}}}\right)\\&\approx 17.6424\,a^{2}.\end{aligned}}
$$

其中 $A$ 表示面積， $a$ 表示邊長。

## 尺規作圖

有一個尺規作圖的方法可以畫出準確的正十五邊形，方法如右圖所示，總計有 36 步。
15邊形