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Like the title. I need to know what the areas of the given shapes are so I can compare if they are roughly equal.

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You will most likely need a script, plugin or extension of some kind.

For Illustator there's a script here: https://gist.github.com/bryanbuchanan/11387501 - which I haven't tested. Measurements appear in a pop-up Script Alert box.

enter image description here

In Inkscape (which is free an Open Source), there is an extension for this which comes pre-installed, so there's nothing extra to install. It's located under Extensions > Visualise Path > Measure Path, then in Measure Path dialog, choose Area as the measurement type. It adds a text label directly to the document.

An example of the Inkscape Measure Path extension in operation

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