Triangles that have the same base and height must have the same area. The area of a triangle is its base multiplied by its height and divide by two. So if the base and height are the same, the area must be too.
The perimeter however can be different even if the height and base are the same. This is because the perimeter also relies on the other two sides of the triangle, which can be different lengths depending on the angle. The picture I've attached shows this pretty well if you're still confused.