Der Schneider nimmt die Messungen is wrong? Messungen is measurements.
In the context of tailoring, one uses Maße nehmen.
Thats completly right. Additional to that. Messungen does not come with the verb nehmen, but it comes with the verb vornehmen (or aufnehmen). Man nimmt Maße. Man nimmt Messungen vor.
There's also a difference in meaning.
Maße are measurements as in the result -- e.g. "25 cm".
Messungen are measurements as in the actions.
This won't accept "Die Schneiderin" :/
The pronunciation example is strange. It says "Masse" (mass) with a short "a". But in "Maße" (measurement) the a is long. It changes the meaning
"Der Schneider nimmt die Messungen vor" should be accepted.