A regular tetrahedron has sides of length s. Show that the surface area, A, of the tetrahedron can be determined using the formula A= square root of 3s^2

Answer 1

The net of a regular tetrahedron consists of 4 equilateral triangles.
Look at one of them:
If the side is s, then the area
= (1/2)(s)(s)sin60°
= (1/2)(√3/2)s^2
= √3/4 s^2
all 4 of them ----> 4(√3/4)s^2
= √3 s^2 , as required