The length of CE is 2, so CDE has the same length base as ABC. Since D is the midpoint of AC, the perpendicular distance from D to BC is half that of the perpendicular distance from A to BC. Thus the height of CDE is half that of ABC.
CDE thus has the same base as ABC and half the height of ABC. Its area is thus half that of ABC.
The area of an equilateral triangle of side length s is (s2√3)/4. So the area of ABC is √3, and the area of CDE is (√3)/2.
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