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Given ABC and BDE are two equilateral triangles and D is the midpoint of BC.
Any two equilateral triangles are similar as each angle is equal to 60°.
Hence ΔABC ~ ΔBDE [AAA similarity theorem]
Recall that the ratio of areas of two similar triangles is equal to ratio of squares of their corresponding sides.

Therefore, ar(ΔABC) = (1/4) × ar(ΔBDE
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