Let's go through the problem step-by-step to find the area of the wall that is not painted red.
### Step 1: Calculate the Area of One Square
Kathleen paints squares, each having a side length of 2.5 feet.
The formula for the area of a square is:
[tex]\[ \text{Area of a square} = \text{side length} \times \text{side length} \][/tex]
So,
[tex]\[ \text{Area of one square} = 2.5 \, \text{feet} \times 2.5 \, \text{feet} = 6.25 \, \text{square feet} \][/tex]
### Step 2: Calculate the Total Area Painted Red
Kathleen paints 3 squares on the wall. To find the total area painted red, we multiply the area of one square by the number of squares painted.
[tex]\[ \text{Total painted area} = \text{Area of one square} \times \text{number of squares} \][/tex]
So,
[tex]\[ \text{Total painted area} = 6.25 \, \text{square feet} \times 3 = 18.75 \, \text{square feet} \][/tex]
### Step 3: Calculate the Area of the Wall Not Painted Red
The total area of the wall is given as 75 square feet. To find the area of the wall that is not painted red, we subtract the total painted area from the total wall area.
[tex]\[ \text{Area of the wall not painted} = \text{Total area of the wall} - \text{Total painted area} \][/tex]
So,
[tex]\[ \text{Area not painted} = 75 \, \text{square feet} - 18.75 \, \text{square feet} = 56.25 \, \text{square feet} \][/tex]
### Final Answer
The area of the wall that is not painted red is:
[tex]\[ 56.25 \, \text{square feet} \][/tex]
