If the sides of a regular triangular pyramid are right triangles and the length of its bottom side is a, then its total area is?

If the sides of a regular triangular pyramid are right triangles and the length of its bottom side is a, then its total area is?

The sides of a regular triangular pyramid are right triangles, so the length of the side edges is √ 2A / 2
One side area is a ^ 2 / 4
The bottom area is √ 3A ^ 2 / 4
So the total area is 3 side areas + bottom areas = (3 + √ 3) a ^ 2 / 4