Textbook Problem

A regular tetrahedron is a regular triangular pyramid in which all faces (lateral faces and base) are congruent. If each edge has length $e$,

a) show that the area of each face is $A=\frac{e^2\sqrt{3}}{4}$.

b) show that the total area of the tetrahedron is $T=e^2\sqrt{3}$.

c) find the total area if each side measures $e=4in.$