Exactly what triangle are you starting with? My understanding of the "Sierpinski triangles" is that you start with an equilateral triangle, divide it into four triangles by connecting the bisectors of the sides, then remove the middle triangle. Then repeat that for the remaining three equilateral triangles. If the original triangle was 1, then the area of the three sierpinski triangles is 3/4. Since that is already less than 1 and you continue by always removing triangles, the total area of all remaining triangles, as you repeat infinitely, cannot be 1.
In fact, after n repetitions, the area of the remaining triangles is which goes to 0. That's why the "Sierpinski triangles" is a fractal set. The measure of a set of dimension "d" is proportional to for some "typical" length x. At each step we are dividing all lengths by 1/3 while multiplying the number of the triangles by 4: the total area would be proportional to . If that will go to infinity. If that will go to 0. We can only get a non-zero finite measure if or . Taking logarithms of both sides, d log(3)= log(4) so d= log(4)/log(3) which is about 1.26. The fractal dimension of the Sierpinski triangles is about 1.26.