Step 1
Given;
[tex]\begin{gathered} \text{Angle of sector=140}^o \\ \text{Diameter of circle=52 inches} \end{gathered}[/tex]Required;
[tex]\begin{gathered} To\text{ find; 1) Arc length} \\ 2)Area_{} \end{gathered}[/tex]Step 2
Find the arc length of the land Juan has cleared by Midday
[tex]\begin{gathered} \text{Arc length=}\frac{\theta}{360}\times2\times\pi\times r \\ r=\frac{\text{ diameter}}{2}=\frac{52}{2}=26\text{inches} \\ \pi=\frac{22}{7} \\ \theta=140 \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Arc length=}\frac{140}{360}\times2\times\frac{22}{7}\times26 \\ \text{Arc length= }\frac{572}{9}=63.555556\text{ inches} \\ \text{Arc length}\approx64inches \end{gathered}[/tex]Hence, the land Juan has cleared by midday has an arc length of about 64 inches
Step 3
Find the area of the land
[tex]\text{Area of a sector=}\frac{\theta}{360}\times\pi\times r^2[/tex][tex]\begin{gathered} \text{Area of the land=}\frac{140}{360}\times\frac{22}{7}\times26^2 \\ \text{Area of the land=}\frac{7436}{9}=826.22222222 \\ \text{Area of the land}\approx826in^2 \end{gathered}[/tex]
Hence, the area of the land he has cleared by midday is about 826in²