[填空题]
Five equilateral triantf:cc,q ,maepq/ 5 vv:dyy9 +a sd 3ulzfpifb:rw4g4:y9*y0igles, each with side length 4 cm, are arranged to form a truss bridge model.This is shown in the following dyiu04lp:g* wf izrfby4s 9:3diagram.
The vectors $ \mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are shown on the diagram.
Find $\mathbf{a} \cdot(\mathbf{a}+\mathbf{b}+2 \mathbf{c}) $.
