Suppose I am given a task to weigh this wall. Neither can I uproot this wall to put it on a weighing scale and measure its weight nor I can place a weighing machine below it.
What should I do then?
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You can measure the volume $V$ and density $\rho$ of the wall and calculate the mass $m$ from this using this formula:
$$m = \rho \cdot V$$
The density can be found by looking up a tabulated value for the specific material used, or by taking a sample of the brick, measuring volume and mass and employing the same formula as above.
It should be noted that the wall is of course not homogenous, it contains spaces with air and mortar, but for an estimation, these can be ignored or factored in roughly.