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Update index.html
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@@ -3558,10 +3558,107 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
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<br>
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<br>
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The base of a tetrahedron is an equilateral triangle.
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</p>
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<br>
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The area of an equilateral triangle equals side / 2 × √(side^2 - ( side / 2 )^2) = side / 2 × √(side^2 - side^2 / 4) = side / 2 × √(( 3 / 4 )side^2) = side / 2 × side × √(3) / 2 = side^2 × √(3) / 4 .
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<math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>A</mi>
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<mo>=</mo>
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<mrow>
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<mfrac>
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<mi>side</mi>
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<mn>2</mn>
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</mfrac>
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<mo>×</mo>
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<msqrt>
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<mrow>
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<msup>
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<mi>side</mi>
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<mn>2</mn>
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</msup>
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<mo>-</mo>
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<msup>
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<mrow>
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<mo>(</mo>
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<mfrac>
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<mi>side</mi>
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<mn>2</mn>
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</mfrac>
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<mo>)</mo>
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</mrow>
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<mn>2</mn>
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</msup>
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</mrow>
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</msqrt>
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</mrow>
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<mo>=</mo>
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<mrow>
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<mfrac>
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<mi>side</mi>
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<mn>2</mn>
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</mfrac>
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<mo>×</mo>
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<msqrt>
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<mrow>
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<msup>
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<mi>side</mi>
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<mn>2</mn>
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</msup>
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<mo>-</mo>
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<mfrac>
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<mrow>
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<msup>
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<mi>side</mi>
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<mn>2</mn>
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</msup>
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</mrow>
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<mn>4</mn>
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</mfrac>
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</mrow>
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</msqrt>
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</mrow>
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<mo>=</mo>
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<mrow>
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<mfrac>
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<mi>side</mi>
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<mn>2</mn>
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</mfrac>
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<mo>×</mo>
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<msqrt>
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<mrow>
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<mfrac>
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<mi>3</mi>
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<mn>4</mn>
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</mfrac>
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<mo>×</mo>
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<msup>
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<mi>side</mi>
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<mn>2</mn>
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</msup>
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</mrow>
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</msqrt>
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</mrow>
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<mo>=</mo>
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<mrow>
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<mfrac>
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<mi>side</mi>
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<mn>2</mn>
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</mfrac>
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<mo>×</mo>
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<mfrac>
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<mrow>
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<msqrt>
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<mi>3</mi>
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</msqrt>
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</mrow>
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<mn>4</mn>
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</mfrac>
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</mrow>
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</mrow>
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</math>
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<br>
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<br>
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<p>
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The height of the tetrahedron equals √(( edge × √(3) / 2 )^2 − ( ( edge × √(3) / 2 ) / 3 )^2 ) =
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<br>
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√( edge^2 × ( 3 / 4 - 3 / 36 ) ) =

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