Most of us know what a piazza is. It means something akin to the town square. In Italy, there may be a main piazza, but there can be many others spread around a city.

La piazza è dedicata al...

The piazza is dedicated to...

all'artista e scultore Michelangelo Buonarroti.

to the artist and sculptor Michelangelo Buonarroti.

Caption 12, In giro per l'Italia - Firenze

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If you look at the dictionary entry above, you will see that there are various connotations of the noun piazza. 

Piazzare is a verb. It can mean "to place" something somewhere.

Qua abbiamo piazzato la macchina da presa.

Here, we placed the camera.

Caption 27, Fratelli Taviani - La passione e l'utopia

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Piazzare often means to sell — to put on the market with success.

Be', questa pietruzza la posso piazzare per una bella cifra.

Well this little rock I can place/sell for a pretty penny.

Caption 42, La Ladra - EP. 1 - Le cose cambiano

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But when we add an S to the beginning as a sort of prefix, the meaning changes. Something is set up or placed and seems stable, but then you displace it: spiazzare. It's generally used figuratively to mean "to catch someone off guard."

So, spiazzare is "to cause someone to feel less stable." You floor them, you take away their certainties, you take them by surprise.

E poi ti spiazzava.

And then she would take you by surprise.

Spiazzava te che eri al suo fianco,

She would totally surprise you, you, who were by her side,

spiazzava il pubblico.

she would floor the audience.

Ma a volte ti accorgevi che spiazzava anche se stessa...

But sometimes you would realize that she took even herself by surprise...

Captions 29-32, Illuminate - Margherita Hack - Part 11

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E io sono abituata a condurre il gioco. Insomma, mi sento spiazzata.

And I am used to leading the game. Basically, I'm flummoxed.

Captions 77-78, Provaci ancora prof! - S1E3 - Una piccola bestia ferita

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