Question 1119151
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Segment DE joins the midpoints of two sides of the equilateral triangle.  Place point F at the midpoint of the third side of the triangle and draw segments DF and EF.  It should be clear that the original equilateral triangle is now composed of 4 congruent equilateral triangles, each with area 1/4 of the original triangle.<br>
So the area of each of the smaller triangles, including triangle ADE, is sqrt(3).