Regular or equilateral tetrahedron – all edges are equal, and the faces, respectively, are equilateral triangles.
The formula for the surface area of an equilateral tetrahedron:
where is the a-side
Rectangular tetrahedron – the angle between all three edges at one vertex is straight, i.e. equal to 90°
The formula for the surface area of a rectangular tetrahedron:
where a,b,c are the sides at an angle of 90°, d,e,f are the sides of the base
Solution:
S1 =
=
=
= 60.5
S2 =
=
=
= 60.5
S3 =
=
=
= 60.5
p =
=
=
= 16.5
S4 = √p·(p-d)·(p-e)·(p-f)
= √16.5·(16.5-11)·(16.5-11)·(16.5-11)
= √16.5·5.5·5.5·5.5
= 52.395
S = S1+S2+S3+S4
= 60.5+60.5+60.5+52.395
=
233.895
a: The area of the entire surface of a rectangular tetrahedron equal to 233.895