Bài 2: Định Lí Đảo Và Hệ Quả Của Định Lí Ta-Lét
Hướng dẫn giải Bài 11 (Trang 63 SGK Toán Hình học 8, Tập 2)
<p><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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2206;</mo><mi>A</mi><mi>B</mi><mi>C</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-mo"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><span id="MJXc-Node-4" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-5" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-6" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> có <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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>C</mi><mo>=</mo><mn>15</mn><mi>c</mi><mi>m</mi></math>"><span id="MJXc-Node-7" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-8" class="mjx-mrow"><span id="MJXc-Node-9" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-10" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-11" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-12" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">15</span></span><span id="MJXc-Node-13" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-14" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span>. Trên đường cao <span id="MathJax-Element-3-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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>H</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>H</mi></math></span></span> lấy các điểm <span id="MathJax-Element-4-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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>,</mo><mi>K</mi></math>"><span id="MJXc-Node-19" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-20" class="mjx-mrow"><span id="MJXc-Node-21" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">I</span></span><span id="MJXc-Node-22" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-23" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">K</span></span></span></span></span> sao cho <span id="MathJax-Element-5-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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>K</mi><mo>=</mo><mi>K</mi><mi>I</mi><mo>=</mo><mi>I</mi><mi>H</mi></math>"><span id="MJXc-Node-24" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-25" class="mjx-mrow"><span id="MJXc-Node-26" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-27" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">K</span></span><span id="MJXc-Node-28" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-29" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">K</span></span><span id="MJXc-Node-30" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">I</span></span><span id="MJXc-Node-31" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-32" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">I</span></span><span id="MJXc-Node-33" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span></span></span></span>. Qua <span id="MathJax-Element-6-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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span> và <span id="MathJax-Element-7-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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></span></span> vẽ các đường <span id="MathJax-Element-8-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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>F</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><mi>C</mi><mo>,</mo><mi>M</mi><mi>N</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><mi>C</mi></math>"><span id="MJXc-Node-40" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-41" class="mjx-mrow"><span id="MJXc-Node-42" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-43" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-44" class="mjx-texatom"><span id="MJXc-Node-45" class="mjx-mrow"><span id="MJXc-Node-46" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-47" class="mjx-texatom"><span id="MJXc-Node-48" class="mjx-mrow"><span id="MJXc-Node-49" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-50" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-51" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-52" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-53" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-54" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span><span id="MJXc-Node-55" class="mjx-texatom"><span id="MJXc-Node-56" class="mjx-mrow"><span id="MJXc-Node-57" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-58" class="mjx-texatom"><span id="MJXc-Node-59" class="mjx-mrow"><span id="MJXc-Node-60" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-61" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-62" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> (h.17)<br /><img src="https://img.loigiaihay.com/picture/2018/0718/b11-trang-63-sgk-toan-8-t2-c2.jpg" /></p>
<p><strong>LG a.</strong></p>
<p>Tính độ dài đoạn thẳng <span id="MathJax-Element-9-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>M</mi><mi>N</mi></math>"><span id="MJXc-Node-63" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-64" class="mjx-mrow"><span id="MJXc-Node-65" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></span></span> và <span id="MathJax-Element-10-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>E</mi><mi>F</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>F</mi></math></span></span>.</p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng: Hệ quả của định lý TaLet, áp dụng kết quả của bài 10.</p>
<p><strong>Lời giải chi tiết:</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mstyle></math> có MN//BC (gt)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mfrac><mrow><mi>M</mi><mo>⁢</mo><mi>N</mi></mrow><mrow><mi>C</mi><mo>⁢</mo><mi>B</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>K</mi></mrow><mrow><mi>A</mi><mo>⁢</mo><mi>H</mi></mrow></mfrac></mstyle></math> (kết quả bài tập 10) (định lý TaLet)<br />Mà AK=KI=IH.<br />Nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>K</mi></mrow><mrow><mi>A</mi><mo>⁢</mo><mi>H</mi></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mfrac><mrow><mi>M</mi><mo>⁢</mo><mi>N</mi></mrow><mrow><mi>C</mi><mo>⁢</mo><mi>B</mi></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>⇒</mo><mi>M</mi><mo>⁢</mo><mi>N</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>⋅</mo><mn>15</mn><mo>=</mo><mpadded><mn>5</mn></mpadded><mo>⁢</mo><mi>cm</mi></mrow><mo>.</mo></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mstyle></math> có EF//BC (gt)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mfrac><mrow><mi>E</mi><mo>⁢</mo><mi>F</mi></mrow><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>I</mi></mrow><mrow><mi>A</mi><mo>⁢</mo><mi>H</mi></mrow></mfrac><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mstyle></math> (định lý TaLet)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>⇒</mo><mi>E</mi><mo>⁢</mo><mi>F</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>⋅</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>⋅</mo><mn>15</mn><mo>=</mo><mpadded><mn>10</mn></mpadded><mo>⁢</mo><mi>cm</mi></mrow><mo>.</mo></math></p>
<p><strong>LG b.</strong></p>
<p>Tính diện tích tứ giác <span id="MathJax-Element-22-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>M</mi><mi>N</mi><mi>F</mi><mi>E</mi></math>"><span id="MJXc-Node-253" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-254" class="mjx-mrow"><span id="MJXc-Node-255" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-256" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span><span id="MJXc-Node-257" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-258" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span>, biết diện tích của <span id="MathJax-Element-23-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"><mo>&#x2206;</mo><mi>A</mi><mi>B</mi><mi>C</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>A</mi><mi>B</mi><mi>C</mi></math></span></span> là <span id="MathJax-Element-24-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>270</mn></math>"><span id="MJXc-Node-265" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-266" class="mjx-mrow"><span id="MJXc-Node-267" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">270</span></span></span></span></span> cm<sup>2</sup></p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng: Hệ quả của định lý TaLet, áp dụng kết quả câu a.</p>
<p><strong>Lời giải chi tiết:</strong></p>
<p>Theo câu a) ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>A</mi><mo>⁢</mo><mi>K</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>H</mi><mo>;</mo><mi>M</mi><mo>⁢</mo><mi>N</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mstyle></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>A</mi><mo>⁢</mo><mi>I</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>H</mi><mo>;</mo><mi>E</mi><mo>⁢</mo><mi>F</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mstyle></math><br />Nên:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>M</mi><mo>⁢</mo><mi>N</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mi>A</mi><mi>K</mi><mo>.</mo><mi>M</mi><mpadded><mi>N</mi></mpadded><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>A</mi><mi>H</mi><mo>⋅</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>B</mi><mpadded><mi>C</mi></mpadded><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mfrac><mn>1</mn><mn>9</mn></mfrac><mo>⋅</mo><mrow><mo>(</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>A</mi><mi>H</mi><mo>.</mo><mi>B</mi><mi>C</mi><mo>)</mo></mrow><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mfrac><mn>1</mn><mn>9</mn></mfrac><mo>⋅</mo><mpadded><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow></msub></mpadded><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mfrac><mn>1</mn><mn>9</mn></mfrac><mo>⋅</mo><mn>270</mn><mo>=</mo><mpadded><mn>30</mn></mpadded><msup><mi>cm</mi><mn>2</mn></msup></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>F</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mi>A</mi><mi>I</mi><mo>.</mo><mi>E</mi><mpadded><mi>F</mi></mpadded><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>A</mi><mi>H</mi><mo>⋅</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>B</mi><mpadded><mi>C</mi></mpadded><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>4</mn><mn>9</mn></mfrac><mo>⋅</mo><mrow><mo>(</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>A</mi><mi>H</mi><mo>.</mo><mi>B</mi><mi>C</mi><mo>)</mo></mrow><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>4</mn><mn>9</mn></mfrac><mo>⋅</mo><mpadded><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow></msub></mpadded><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>4</mn><mn>9</mn></mfrac><mo>⋅</mo><mn>270</mn><mo>=</mo><mpadded><mn>120</mn></mpadded><msup><mi>cm</mi><mn>2</mn></msup></math><br />Do đó <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mrow><mi>M</mi><mo>⁢</mo><mi>N</mi><mo>⁢</mo><mi>F</mi><mo>⁢</mo><mi>E</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>F</mi></mrow></msub><mo>-</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>M</mi><mo>⁢</mo><mi>N</mi></mrow></msub><mo>=</mo><mn>120</mn><mo>-</mo><mn>30</mn><mo>=</mo><mpadded><mn>90</mn></mpadded><mo>⁢</mo><msup><mi>cm</mi><mn>2</mn></msup></math></p>
<p> </p>
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