If we have triangular pyramid with a side of s and all the faces and the base are equilateral triangles, then the formula for the total surface area is
SA = 3As + Ab
Where As is the area of the three faces
and
Ab is the area of the base
Since the triangles are equilateral, the surface area in terms of s is
SA = 3 (√3/ 4) s² + √3/ 4 s²
SA = √3 s²
