Its area is 1/2×2×√3=√3.

The area of this triangle is also equal to the sum of the areas of three small triangles.

1/2×2×PD+ 1/2×2×PE+ 1/2×2×PF

=PD+PE+PF

=√3

As shown in the figure, do GH//BC, LM//AC, JK//AB to P.

You should be able to see the rest. Adjacent small black triangles and small white triangles have the same area.

Examples: △BPG and △BPJ have equal areas (diagonal principle of parallelogram), △JPD and △MPD have equal areas (△JPM is a regular triangle), and so on.

It can be seen that the final black and white area accounts for half, so the shadow area is 1/2 * 1/2 * 2 * SIN 60 = (root number 3)/2.