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In the figure above, $\overline{AB} \parallel \overline{DE}$ and $\overline{AE}$ intersects $\overline{BD}$ at point $C.$ What is the perimeter of $\triangle CED?$

(A) $\ \ 6.75$ (B) $\ \ 12$ (C) $\ \ 13$ (D) $\ \ 19.5$ (E) $\ \ 22.5$

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