This image demonstrates what base edge and slant height are.

Look at the lateral triangle that slant height is drawn. Its base is 3 inches, like other base edges. All base edges are equivalent since it's a regular triangular pyramid.

And we know that slant height is 4 inches. Aha! It's so easy, we have the base and the height of one of the lateral triangles. Its area is square inches.

If the area of one lateral triangle is 6 square inches, and there are 3 of them, what can the total lateral area be? As you see, there are 3 equivalent lateral triangles, each of them being 6 square inches. Then the total area is square inches