Is the bottom and side of a regular triangular pyramid equal? How can I find his height quickly? ...

The four faces of a regular triangular pyramid are regular triangles, and their sides are equal, so the four regular triangles are congruent. Let the side length of the regular triangular pyramid be x, then the photography of the fixed point at the bottom of the regular triangular pyramid is the center of gravity of the triangle at the bottom, and then there is h = √ [(x 2-x 2/3) = √ 6x/3.