Question 1189506
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Answer: (25/4)*sqrt(3)


Reason:
The altitude line AD is also a median for the equilateral triangle ABC. Median lines cut the area in half since they cut the base in half, while the height stays the same. 


So we have 
area of triangle ABD = (1/2)*(area of triangle ABC)
Then furthermore,
area of triangle ABE = (1/2)*(area of triangle ABD)


So overall,
area of triangle ABE = (1/2)*(1/2)*(area of triangle ABC)
area of triangle ABE = (1/4)*(area of triangle ABC)
area of triangle ABE = (1/4)*25*sqrt(3)
area of triangle ABE = (25/4)*sqrt(3)
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