Many Black Triangles.

If $AB=16$ , then the side of each small black triangle is $2$ . We have $8$ small black triangles on side $AB$ . We also know the area of any equilateral triangle is $\frac{s^2\sqrt{3}}{4}\implies$ the area of one small black triangle is $\frac{4\sqrt{3}}{4}=\sqrt{3}$ . By counting, there are $27$ small black triangles.

Thus, the area of the all the black triangles is $27\times \sqrt{3}=27\sqrt{3}.$