SOLUTION: Equilateral triangle ABC with area 25√3 m^2 has altitude line AD. Triangle ABD has a median line AE. What is the area, in m^2, of Triangle ABE?

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Question 1189506: Equilateral triangle ABC with area 25√3 m^2 has altitude line AD. Triangle ABD has a median line AE. What is the area, in m^2, of Triangle ABE?
Answer by math_tutor2020(3817) About Me  (Show Source):
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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)