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ABC and BDE are two equilateral triangle...

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then, `ar (DeltaBDE) = (1)/(4) ar (DeltaABC)`.

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To solve the problem, we need to show that the area of triangle BDE is equal to one-fourth of the area of triangle ABC, given that D is the midpoint of side BC in the equilateral triangle ABC. ### Step-by-Step Solution: 1. **Identify the triangles**: We have two equilateral triangles, ABC and BDE, with D as the midpoint of side BC. 2. **Assign lengths**: Let the side length of triangle ABC be denoted as \( s \). Since ABC is equilateral, all sides are equal, so \( AB = BC = CA = s \). ...
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