To solve this problem, we need to find the area of the wall first and then determine half of that area since Marcus is painting half of the wall blue. Here are the detailed steps:
1. Convert Mixed Numbers to Improper Fractions:
- The height of the wall is given as [tex]\( 8 \frac{2}{5} \)[/tex] feet.
To convert the mixed number to an improper fraction:
[tex]\[
8 \frac{2}{5} = 8 + \frac{2}{5} = \frac{40}{5} + \frac{2}{5} = \frac{42}{5} = 8.4 \text{ feet}
\][/tex]
- The length of the wall is given as [tex]\( 18 \frac{1}{3} \)[/tex] feet.
To convert the mixed number to an improper fraction:
[tex]\[
18 \frac{1}{3} = 18 + \frac{1}{3} = \frac{54}{3} + \frac{1}{3} = \frac{55}{3} = 18.333333333333332 \text{ feet}
\][/tex]
2. Calculate the Area of the Wall:
- Now, we determine the area by multiplying the height by the length:
[tex]\[
\text{Area of the wall} = \text{Height} \times \text{Length} = 8.4 \times 18.333333333333332 = 154.0 \text{ square feet}
\][/tex]
3. Calculate the Blue Area:
- Since Marcus is painting half of the wall blue, we take half of the total area of the wall:
[tex]\[
\text{Blue area} = \frac{1}{2} \times \text{Area of the wall} = \frac{1}{2} \times 154.0 = 77.0 \text{ square feet}
\][/tex]
Therefore, the area of the wall that will be painted blue is [tex]\( 77.0 \)[/tex] square feet.
