Should you need noncongruent triangles of equal area, here’s how to get them. Segment BX is their altitude (height). Segments AC, CD, DE, EF, FG, GH, and HJ (triangle bases) are constructed to be congruent, so each of these non-overlapping, differently-colored triangles has the same area because they have the same base and height lengths. Extend AJ as a line, add more points, using the same spacing, and you can have as many such triangles as you desire.

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