How to determine the Absorption coefficient of the material shown as follow? paper plus + air? Acoustic absorption refers to the process by which a material, structure, or object takes in sound energy when sound waves are encountered, as opposed to reflecting the energy.
wiki gives a table for Absorption coefficients of common materials
How to determine the Absorption coefficient of the material shown as follow? paper plus + air?

 A: Absorption coefficients are empirically determined.
I had a very interesting visit to an acoustics lab many years ago, and got to see this very thing in person. Often the work is conducted in a reverberation room:

The goal is to approximate a diffuse, random-incidence sound field. A speaker plays a known sound in the room. The rectangular panel in the image can be replaced with a test panel (like your cardboard.)
I won't quote the classic work on the subject (Christler and Snyder 1930) too extensively - you should have a look yourself. The basic idea is that you have two difference absorption coefficients $a_1$ (the room), and $a_2$ (the panel) representing different surface areas $S_1$ (the room without the panel) and $S_2$ (the panel). The sound source's intensity in the room ($A_1$) doesn't change. 
The authors write that this reduces the acoustic intensity of the of the room from:

$\frac{4 A_1}{a_1 Sv}$ to $\frac{4 A_1}{(a_1 S_1 + a_2 S_2)v}$

Note that the latter must be smaller, because $a_2$ is larger. 
They then relate intensity to decay time, allowing $a_2$ to be solved:

$a_1 S_1 + a_2 S_2 = \frac{4V \ 2.3 \ log_{10}(\frac{E_1}{E_2})}{v(t^{1}_{2} -t^{'}_{1})}$

As you can see this requires quite a few known values: the surface area of the room ($S$), it's volume ($V$), the measured intensity in the room in both scenarios ($E_1, E_2$), and the decay times ($t^{'}_1, t^{1}_{2}$). In other words, it's not a trivial task to determine absorption coefficients. 
