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Update index.html
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index.html

Lines changed: 15 additions & 25 deletions
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@@ -3656,34 +3656,36 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
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</mrow>
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<mo>=</mo>
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<mrow>
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<msup>
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<mi>edge</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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<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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<msup>
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<mo>×</mo>
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<mi>edge</mi>
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<mn>2</mn>
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</msup>
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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 style="margin:12px;">The height of the tetrahedron is also calculable via trigonometry.
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</p>
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<br>
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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>H</mi>
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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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<mo>(</mo>
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<mrow>
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<mo>(</mo>
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<mi>edge</mi>
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<mo>×</mo>
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<mfrac>
@@ -3693,6 +3695,7 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
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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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<mo>-</mo>
@@ -3708,8 +3711,10 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
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<mn>6</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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</msqrt>
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</mrow>
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</math>
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<br>
@@ -3757,26 +3762,11 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
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</mrow>
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</mrow>
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</math>
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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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<br>
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√( edge^2 × ( 27 / 36 - 3 / 36 ) ) =
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<br>
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√( edge^2 × ( 24 / 36 ) ) =
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√( 2 / 3 ) × edge.
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<br>
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The base of a tetrahedron multiplied by its height equals ( edge^2 × √( 3 / 4 ) ) × ( edge × √( 2 / 3 ) ) = edge^3 × √(2) / 4 .
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<br>
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The volume of a pyramid equals base × height × √(2) / 4 .
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<br>
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( √(2) / 4 )^2 = 2 / 16 = 1 / 8
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<p style="margin:12px;">The volume of a pyramid equals base × height × √(2) / 4 .
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</p>
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<br>
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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>V</mi>

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