The short answer is that the area must be equal to the area of the original triangle, because the Sierpinski gasket (all the “unshaded” regions) has area zero. See Sierpinski Gasket AreaBut we can also write a geometric series. Say the initial triangle has area 1. Then the largest shaded triangle had area 1/4. (This is easily shown using symmetry.) Each of the next smallest triangles occupy 1/16 of the original area, and there are 3 of them. Then 1/64 of the area, with 9 triangles.At each iteration, there are 3 times as many triangles but each occupies 1/4 of the previous triangle’s area. That gives a geometric series with ratio 3/4 for the total area: