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we know that
the area of the floor is equal to the area of a rectangle
so
Area of the floor[tex]=L*W[/tex]
where
L is the length side of the floor
W is the width side of the floor
[tex] L=100\frac{3}{4} ft\\\\ L=(100*4+3)/4\\\\ L=\frac{403}{4} ft [/tex]
[tex] W=75\frac{1}{2} ft\\\\ W=(75*2+1)/2\\\\ W=\frac{151}{2} ft [/tex]
Area of the floor[tex] =\frac{403}{4} *\frac{151}{2} [/tex]
Area of the floor[tex]= \frac{60,853}{8} [/tex]
Area of the floor=[tex] 7,606.625 [/tex] ft²
therefore
the answer is
the area of the floor is [tex] 7,606.625 [/tex] ft²