21.1 As shown in the figure, five equilateral triangles are arranged on the same side of a straight line on the plane. The side length of each triangle is $2 \sqrt{3}$, and the midpoint of the base of each triangle is the vertex of the next triangle. The area of the region covered by these five triangles is
(A) 10 .
(B) 12 .
(C) 15 .
(D) $10 \sqrt{3}$.
(E) $12 \sqrt{3}$.
[Sol] Note that each equilateral triangle can be equally divided into four congruent smaller equilateral triangles, which is exactly the overlapping part of two equilateral triangles.

Obviously, the overlapping part of these 5 equilateral triangles is 4 smaller equilateral triangles, which exactly form one equilateral triangle.
That is, the area covered by the five triangles is the area of four equilateral triangles:
$$
4 \cdot \frac{\sqrt{3}}{4} \cdot(2 \sqrt{3})^{2}=12 \sqrt{3} \text {. }
$$

Therefore, the answer is $(E)$.