Bài 6: Diện Tích Đa Giác
Hướng dẫn giải Bài 37 (Trang 130 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Thực hiện các phép đo cần thiết (chính xác đến từng m) để tính diện tích hình <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi><mi>C</mi><mi>D</mi><mi>E</mi></math>"><span id="MJXc-Node-1" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-2" class="mjx-mrow"><span id="MJXc-Node-3" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-4" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-5" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-6" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-7" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> (h.<span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>152</mn></math>"><span id="MJXc-Node-8" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-9" class="mjx-mrow"><span id="MJXc-Node-10" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">1</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>52</mn></math></span></span>).</p>
<p><img src="https://img.loigiaihay.com/picture/2018/0716/b37-trang-130-sgk-toan-8-t-1-c2.jpg" /></p>
<p>Lời giải chi tiết<br />Đa giác ABCDE được chia thành tam giác ABC, hai tam giác vuông AHE, DKC và hình thang vuông HKDE.<br />Thực hiện phép đo chính xác đến mm ta được:</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo></mo><mi>B</mi><mo></mo><mi>G</mi><mo>=</mo><mn>19</mn><mo></mo><mi>m</mi><mo></mo><mi>m</mi><mo>,</mo><mi>A</mi><mo></mo><mi>C</mi><mo>=</mo><mn>48</mn><mo></mo><mi>m</mi><mo></mo><mi>m</mi><mo>,</mo><mi>A</mi><mo></mo><mi>H</mi><mo>=</mo><mn>8</mn><mo></mo><mi>m</mi><mo></mo><mi>m</mi><mo>,</mo><mi>H</mi><mo></mo><mi>K</mi><mo>=</mo><mn>18</mn><mo></mo><mi>m</mi><mo></mo><mpadded><mi>m</mi></mpadded><mo></mo><mspace linebreak="newline"></mspace><mo></mo><mi>K</mi><mo></mo><mi>C</mi><mo>=</mo><mn>22</mn><mo></mo><mi>m</mi><mo></mo><mi>m</mi><mo>,</mo><mi>E</mi><mo></mo><mi>H</mi><mo>=</mo><mn>16</mn><mo></mo><mi>m</mi><mo></mo><mi>m</mi><mo>,</mo><mi>K</mi><mo></mo><mi>D</mi><mo>=</mo><mn>23</mn><mo></mo><mi>m</mi><mo></mo><mpadded><mi>m</mi></mpadded><mo></mo><mspace linebreak="newline"></mspace><mo></mo><msub><mi>S</mi><mrow><mi>A</mi><mo></mo><mi>B</mi><mo></mo><mi>C</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mi>B</mi><mo></mo><mi>G</mi><mo>⋅</mo><mi>A</mi><mo></mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>19.48</mn><mo>=</mo><mn>456</mn><mo></mo><mrow><mo>(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mo></mo><mspace linebreak="newline"></mspace><msub><mi>S</mi><mrow><mi>A</mi><mo></mo><mi>H</mi><mo></mo><mi>E</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mi>A</mi><mo></mo><mi>H</mi><mo>.</mo><mi>H</mi><mo></mo><mi>E</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mn>8.16</mn><mo>=</mo><mn>64</mn><mo></mo><mrow><mo>(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mo></mo><mspace linebreak="newline"></mspace><msub><mi>S</mi><mrow><mi>D</mi><mo></mo><mi>K</mi><mo></mo><mi>C</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mi>K</mi><mo></mo><mi>C</mi><mo>⋅</mo><mi>K</mi><mo></mo><mi>D</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>22.23</mn><mo>=</mo><mn>253</mn><mo></mo><mrow><mo>(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mo></mo><mspace linebreak="newline"></mspace><msub><mi>S</mi><mrow><mi>H</mi><mo></mo><mi>K</mi><mo></mo><mi>D</mi><mo></mo><mi>E</mi></mrow></msub><mo>=</mo><mfrac><mrow><mrow><mo>(</mo><mi>H</mi><mo></mo><mi>E</mi><mo>+</mo><mi>K</mi><mo></mo><mi>D</mi><mo>)</mo></mrow><mo>.</mo><mi>H</mi><mo></mo><mi>K</mi></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mrow><mo>(</mo><mn>16</mn><mo>+</mo><mn>23</mn><mo>)</mo></mrow><mo></mo><mn>.18</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mpadded><mn>351</mn></mpadded><mo></mo><mo></mo><mrow><mo>(</mo><mi>m</mi><mo></mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mo></mo><mspace linebreak="newline"></mspace><mi>D</mi><mi>o</mi><mo> </mo><mi>đ</mi><mi>ó</mi><mspace linebreak="newline"></mspace><msub><mi>S</mi><mrow><mi>A</mi><mo></mo><mi>B</mi><mo></mo><mi>C</mi><mo></mo><mi>D</mi><mo></mo><mi>E</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>A</mi><mo></mo><mi>B</mi><mo></mo><mi>C</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>A</mi><mo></mo><mi>H</mi><mo></mo><mi>E</mi></mrow></msub><mo>+</mo><mpadded><msub><mi>S</mi><mrow><mi>D</mi><mo></mo><mi>K</mi><mo></mo><mi>C</mi></mrow></msub></mpadded><mo></mo><mi mathvariant="normal">&</mi><mo>+</mo><msub><mi>S</mi><mrow><mi>H</mi><mo></mo><mi>K</mi><mo></mo><mi>D</mi><mo></mo><mi>E</mi></mrow></msub><mo>=</mo><mn>456</mn><mo>+</mo><mn>64</mn><mo>+</mo><mn>253</mn><mo>+</mo><mn>351</mn><mo>=</mo><mn>1124</mn><mo></mo><mrow><mo>(</mo><mi>m</mi><mo></mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mo></mo><mspace linebreak="newline"></mspace><mi>V</mi><mo></mo><mi>ậ</mi><mi>y</mi><mo></mo><msub><mi>S</mi><mrow><mi>A</mi><mo></mo><mi>B</mi><mo></mo><mi>C</mi><mo></mo><mi>D</mi><mo></mo><mi>E</mi></mrow></msub><mo>=</mo><mn>1124</mn><mo></mo><mrow><mo>(</mo><mi>m</mi><mo></mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mo></mo><mn>15766</mn></math></p>
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