If two triangles have the same area, their shapes must be exactly the same?

No, if the results are all equal to 6
The first type: 1 × 12 △ 2 = 6
The second: 3 × 4 △ 2 = 6

When two triangles are equal in area, they must be equal in height and equal in base______ (judge right or wrong)

It is known from the analysis that the areas of two triangles are equal, not necessarily equal to the base and height. For example, the areas of two triangles with the base and height of 4 and 3 respectively are equal, but the base and height are not equal

Is it right or wrong that two triangles with the same base and height, regardless of their shape, must have the same area?

Yes
It's the same height as the bottom~
If you learn congruent triangles or similar triangles
I see^

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