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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -3656,34 +3656,36 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
36563656</ mrow >
36573657 < mo > =</ mo >
36583658< mrow >
3659- < msup >
3660- < mi > edge</ mi >
3661- < mn > 2</ mn >
3662- </ msup >
3663- < mo > ×</ mo >
36643659 < mfrac >
3665- < mrow >
3660+ < mrow >
36663661 < msqrt >
36673662 < mi > 3</ mi >
36683663 </ msqrt >
36693664 </ mrow >
36703665 < mn > 4</ mn >
36713666 </ mfrac >
3672- </ mrow >
3667+ < msup >
3668+ < mo > ×</ mo >
3669+ < mi > edge</ mi >
3670+ < mn > 2</ mn >
3671+ </ msup >
3672+ </ mrow >
3673+ </ mrow >
36733674</ math >
36743675< br >
36753676< br >
36763677< p style ="margin:12px; "> The height of the tetrahedron is also calculable via trigonometry.
36773678</ p >
3679+ < br >
36783680< math style ="margin:12px; " xmlns ="http://www.w3.org/1998/Math/MathML ">
36793681 < mrow >
36803682 < mi > H</ mi >
36813683 < mo > =</ mo >
36823684< msqrt >
36833685< mrow >
36843686< msup >
3685- < mo > (</ mo >
36863687< mrow >
3688+ < mo > (</ mo >
36873689< mi > edge</ mi >
36883690 < mo > ×</ mo >
36893691 < mfrac >
@@ -3693,6 +3695,7 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
36933695 < mn > 2</ mn >
36943696 </ mfrac >
36953697 < mo > )</ mo >
3698+ </ mrow >
36963699 < mn > 2</ mn >
36973700 </ msup >
36983701< mo > -</ mo >
@@ -3708,8 +3711,10 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
37083711 < mn > 6</ mn >
37093712 </ mfrac >
37103713 < mo > )</ mo >
3714+ </ mrow >
37113715 < mn > 2</ mn >
37123716 </ msup >
3717+ </ msqrt >
37133718 </ mrow >
37143719</ math >
37153720< br >
@@ -3757,26 +3762,11 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
37573762</ mrow >
37583763 </ mrow >
37593764</ math >
3760- < p >
3761- The height of the tetrahedron equals √(( edge × √(3) / 2 )^2 − ( ( edge × √(3) / 2 ) / 3 )^2 ) =
3762- < br >
3763- √( edge^2 × ( 3 / 4 - 3 / 36 ) ) =
3764- < br >
3765- √( edge^2 × ( 27 / 36 - 3 / 36 ) ) =
37663765< br >
3767- √( edge^2 × ( 24 / 36 ) ) =
37683766< br >
3769- √( 2 / 3 ) × edge.
3770- < br >
3771- < br >
3772- The base of a tetrahedron multiplied by its height equals ( edge^2 × √( 3 / 4 ) ) × ( edge × √( 2 / 3 ) ) = edge^3 × √(2) / 4 .
3773- < br >
3774- < br >
3775- The volume of a pyramid equals base × height × √(2) / 4 .
3776- < br >
3777- < br >
3778- ( √(2) / 4 )^2 = 2 / 16 = 1 / 8
3767+ < p style ="margin:12px; "> The volume of a pyramid equals base × height × √(2) / 4 .
37793768</ p >
3769+ < br >
37803770< math style ="margin:12px; " xmlns ="http://www.w3.org/1998/Math/MathML ">
37813771 < mrow >
37823772 < mi > V</ mi >
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