If she wants one fourth of the dimensions of the room for the corner, that means the area will be 1/16 (one fourth squared) of the whole bedroom. The area of the whole bedroom is 8 x 12 = 96. The area of the corner would be 96 / 16 = 6 sq ft.
Or you can do (one fourth of 8) x (one fourth of 12) = 2 x 3 = 6 sq ft.
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