Update index.html

Author: Gmac4247

index.html

@@ -2902,7 +2902,7 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
 </math>
 <br>
 <br>
-<p style="margin:12px;">The slant shape comes with a triangular vertical cross section. 
+<p style="margin:12px;">The slant shape has a triangular vertical cross section. 
 <br>
 The area of a cone's vertical cross section is the half of a cylinder's with equal base and height. 
 <br>
@@ -3566,22 +3566,22 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
     <mo>=</mo>
 <mrow>
 <mfrac>
-<mi>side</mi>
+<mi>edge</mi>
 <mn>2</mn>
 </mfrac>
     <mo>×</mo>
       <msqrt>
 		<mrow>
 		<msup>
-      <mi>side</mi>
+      <mi>edge</mi>
       <mn>2</mn>
 		</msup>
 		<mo>-</mo>
 		<msup>
 		<mrow>
 		<mo>(</mo>
 	<mfrac>
-<mi>side</mi>
+<mi>edge</mi>
 <mn>2</mn>
 			</mfrac>
 			<mo>)</mo>
@@ -3594,21 +3594,21 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
 	<mo>=</mo>
 <mrow>
 <mfrac>
-<mi>side</mi>
+<mi>edge</mi>
 <mn>2</mn>
 </mfrac>
     <mo>×</mo>
       <msqrt>
 		<mrow>
 		<msup>
-      <mi>side</mi>
+      <mi>edge</mi>
       <mn>2</mn>
 		</msup>
 		<mo>-</mo>
 		<mfrac>
 		<mrow>
 		<msup>
-      <mi>side</mi>
+      <mi>edge</mi>
       <mn>2</mn>
 		</msup>
 		</mrow>
@@ -3618,9 +3618,12 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
       </msqrt>
 </mrow>
 	<mo>=</mo>
+	<br>
+<br>
+<mo>=</mo>
 <mrow>
 <mfrac>
-<mi>side</mi>
+<mi>edge</mi>
 <mn>2</mn>
 </mfrac>
     <mo>×</mo>
@@ -3632,7 +3635,7 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
 		</mfrac>
 		<mo>×</mo>
 		<msup>
-      <mi>side</mi>
+      <mi>edge</mi>
       <mn>2</mn>
 		</msup>
 		</mrow>
@@ -3641,7 +3644,7 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
 		<mo>=</mo>
 <mrow>
 <mfrac>
-<mi>side</mi>
+<mi>edge</mi>
 <mn>2</mn>
 </mfrac>
     <mo>×</mo>
@@ -3658,6 +3661,71 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
 </math>
 <br>
 <br>
+<p style="margin:12px;">The height of the tetrahedron is also calculable via trigonometry.
+</p>
+<math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
+   <mrow>
+ <mi>H</mi>
+    <mo>=</mo>
+<mrow>
+<msqrt>
+<mrow>
+<msup>
+<mrow>
+<mfrac>
+<mrow>
+<mi>edge</mi>
+    <mo>×</mo>
+      <msqrt>
+		<mn>3</mn>
+	  </msqrt>
+</mrow>
+	<mn>2</mn>
+</mrow>
+	<mn>2</mn>
+	  </msup>
+<mo>-</mo>
+<msup>
+<mrow>
+<mfrac>
+<mrow>
+<mi>edge</mi>
+    <mo>×</mo>
+      <msqrt>
+		<mn>3</mn>
+	  </msqrt>
+</mrow>
+	<mn>6</mn>
+</mrow>
+	<mn>2</mn>
+	  </msup>
+</mrow>
+</msqrt>
+</mrow>
+<mo>=</mo>
+<mrow>
+<msqrt>
+<mrow>
+<msup>
+<mrow>
+<mfrac>
+<mrow>
+<mi>edge</mi>
+    <mo>×</mo>
+      <msqrt>
+		<mn>3</mn>
+	  </msqrt>
+</mrow>
+	<mn>2</mn>
+</mrow>
+	<mn>2</mn>
+	  </msup>
+</mrow>
+</msqrt>
+</mrow>
+<mo>=</mo>
+</mrow>
+</math>
 <p>
 The height of the tetrahedron equals √(( edge × √(3) / 2 )^2 − ( ( edge × √(3) / 2 ) / 3 )^2 ) = 
 <br>