To determine how many square feet of the wall Marcus will paint blue, we need to follow these steps:
1. Convert the mixed numbers into improper fractions or decimal form:
The height of the wall is given as [tex]\( 8 \frac{2}{5} \)[/tex] feet.
To convert [tex]\( 8 \frac{2}{5} \)[/tex] into decimal form:
[tex]\[
8 \frac{2}{5} = 8 + \frac{2}{5} = 8 + 0.4 = 8.4
\][/tex]
Therefore, the height of the wall is [tex]\( 8.4 \)[/tex] feet.
The length of the wall is given as [tex]\( 18 \frac{1}{3} \)[/tex] feet.
To convert [tex]\( 18 \frac{1}{3} \)[/tex] into decimal form:
[tex]\[
18 \frac{1}{3} = 18 + \frac{1}{3} = 18 + 0.3333333... \approx 18.3333
\][/tex]
Therefore, the length of the wall is [tex]\( 18.3333 \)[/tex] feet.
2. Calculate the total area of the wall:
The total area of the wall is calculated by multiplying the height by the length.
[tex]\[
\text{Total area} = \text{height} \times \text{length} = 8.4 \, \text{feet} \times 18.3333 \, \text{feet} = 154 \, \text{square feet}
\][/tex]
Therefore, the total area of the wall is [tex]\( 154 \)[/tex] square feet.
3. Determine the area that will be painted blue:
Marcus paints [tex]\(\frac{1}{2}\)[/tex] of the wall blue.
To find the area painted blue, we calculate:
[tex]\[
\text{Blue area} = \text{Total area} \times \frac{1}{2} = 154 \, \text{square feet} \times \frac{1}{2} = 77 \, \text{square feet}
\][/tex]
Therefore, the area of the wall that will be painted blue is [tex]\( 77 \)[/tex] square feet. Thus, the answer to the question is:
[tex]\[ \boxed{77} \][/tex]
