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nice intro. the "diamond" shape you see is built using either hard walls (boundary) or false walls (treatment) depending on the available space, treatments needed, designer preferences, etc. whereas a rectangular shape is generally easier to compute the appropriate size before constructing it. rectangular rooms also tend to be easier (sometimes less expensive) to construct as most builders have experience doing that type of construction. as far as details, we'd need a lot more in terms of the existing space you have available, goals in terms of isolation, etc. there is a read me "sticky" on this forum which can help you to list the details which will help people here be more effective in providing you with answers.

do you have a floor plan of the house?

no dimensions... unless the ones in your initial post are it. if so, what is the 7.5? 7' 6"? if so, why build such a low room? typically if you can build for purpose, no less than 10' finished (3.1m) is decent.