Step1: Convert mixed numbers to improper fractions
Wall length: $11\frac{1}{2} = \frac{23}{2}$ feet, wall height: $8\frac{1}{2} = \frac{17}{2}$ feet
Door width: $3 = \frac{3}{1}$ feet, door height: $6\frac{3}{4} = \frac{27}{4}$ feet
Step2: Calculate wall area (including door)
Area = length × height
$\text{Wall Area} = \frac{23}{2} \times \frac{17}{2} = \frac{391}{4}$ square feet
Step3: Calculate door area
Area = width × height
$\text{Door Area} = \frac{3}{1} \times \frac{27}{4} = \frac{81}{4}$ square feet
Step4: Calculate paintable area
$\text{Paintable Area} = \frac{391}{4} - \frac{81}{4} = \frac{310}{4} = \frac{155}{2} = 77.5$ square feet
Step5: Compare to paint coverage
Paint covers 100 square feet, $77.5 < 100$