Area of a quadratic differential ($\Vert q{\Vert }_1={\int }_X|q|$)

The area of the flat metric of a quadratic differential is ${\int }_X|q|$. Multiplying $q$ by a scalar $a$ multiplies this area by $|a|$ and lengths by $|a{|}^{1/2}$. It is preserved by the SL2R action on differentials.