Right Tetrahedron: de Gua Theorem

​
perpendicular edges(red in the graphic)
j
6
k
8
l
9
face areas
a
24
2
a
576
b
27
2
b
729
c
36
2
c
1296
d
51
2
d
2601
In a right tetrahedron with right triangle faces of area
a
,
b
and
c
and the fourth face of area
d
,
2
a
+
2
b
+
2
c
=
2
d
(de Gua theorem).

External Links

de Gua's Theorem (Wolfram MathWorld)
Pythagorean Theorem (Wolfram MathWorld)
Trirectangular Tetrahedron (Wolfram MathWorld)
Right-Angled Tetrahedron
Pythagorean Theorem 3D

Permanent Citation

Ed Pegg Jr
​
​"Right Tetrahedron: de Gua Theorem"​
​http://demonstrations.wolfram.com/RightTetrahedronDeGuaTheorem/​
​Wolfram Demonstrations Project​
​Published: November 21, 2018