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Say we got three geometries, triangle, square, and circle. If I want to express their shapes and sizes are different. Please help me check which one below may be wrong.

1 The triangle, square, and circle have a different shape.

2 The triangle, square, and circle have different shape s.

3 The triangle, square, and circle are of different size s.

4 The triangle, square, and circle are of a (can I ignore 'a' here?) different size.

5 The triangle, square, and circle have ... VS The triangle, the square, and the circle have ...

Sorry, however, I hope I have described my questions clearly for you.

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I assume you are talking about three particular shapes, and not just these three shapes in general. If you are just comparing ALL triangles, squares, and circles, then you would most likely want to to use an "s" as I just did in this sentence.

Now let's look at your sentences.

1 The triangle, square, and circle have a different shape.

Incorrect. There are three subjects, but the second half of your sentence is singular.

2 The triangle, square, and circle have different shapes.

Correct.

3 The triangle, square, and circle are of different sizes.

Correct. But you could simplify it to "the triangle, square, and circle are different sizes."

4 The triangle, square, and circle are of a (can I ignore 'a' here?) different size.

Incorrect for the same reason as #1. And if the subject was, in fact, singular, you could not ignore the 'a.'

5 The triangle, square, and circle have ... VS The triangle, the square, and the circle have ...

While it is grammatically correct to repeat "the" each time, there is no need for it. And in English we like to keep things as simple as possible, while still maintaining the same meaning. It is best to only use "the" once in this sentence.

I'm not sure what the purpose of this is, but just as a comment, both statements can easily be combined into one short sentence: The triangle, square, and circle all have different shapes and sizes.

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    I think that the most correct way to say it is "The triangle, square, and circle each have a different shape." Commented Sep 26, 2017 at 7:33
  • @MaxWilliams 'Each' is an adverb in the sentence you said? Can I understand its role as 'Each' is used here for changing the meaning of the whole sentence? Commented Sep 26, 2017 at 8:04
  • @KumaAra I think it is correct if I say ' they both are of a different size'. Commented Sep 26, 2017 at 8:10
  • "both" implies togetherness. "Each" emphasises their individuality. If I say "Each is a different size" it's like saying "Every one of them is a different size". "both" doesn't make sense here as there are three things, but if there were two, and you said "They are both a different size", that creates the question "Compared to what?". The use of "both" puts them in a group together, and you're then saying that all members of the group are different to something else. This distinction is lost on many people, meaning that "both" is often misused. Commented Sep 26, 2017 at 8:23
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    Consider "Tom and Jane both have an ice cream". Are they sharing the same ice cream? Possibly - this is the more formally correct interpretation, but it's a bit ambiguous. On the other hand, consider "Tom and Jane each have an ice cream". Now we know that there are two ice creams - they have one each. Commented Sep 26, 2017 at 8:25

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