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How do I retrieve the area of a place which I've already calculate the NDVI index?

The thing is that I just need the area of the pixels that have values between 0.5 to 0.8 (It is a Landsat 8 image).

I'm trying to do the job in QGIS.

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Your problem is the vectorization of an area that is defined by some criteria in a raster file. That could be done by meany means, but the simplest in QGIS is with:

Raster->Conversion->Polygonize (Raster to vector)

You could have a look to this answer: Calculating area of rasters in QGIS? it will lead you to what you need.

A relevant criterion should be the minumum size of the polygonized area and the way to define smoother areas than coarse ones given sometime by the index.

You should give a try with Grass https://grass.osgeo.org/grass72/manuals/r.to.vect.html

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