ANSWER:
8 square meters
STEP-BY-STEP EXPLANATION:
To calculate the area of the sector, we must first calculate the area of the entire circle and then by means of a proportion, knowing that the entire area is 360° and the sector is 45°, we could determine the area we need.
Just like this:
[tex]\begin{gathered} A_c=\pi\cdot r^2 \\ \\ \text{ We replacing:} \\ \\ A_c=\pi\cdot8^2=64\pi \\ \\ \text{ Therefore, we calculate the value of the area of the sector as follows:} \\ \\ A_s=64\pi\cdot\frac{45\degree}{360\degree} \\ \\ A_s=8\pi\text{ square meter} \end{gathered}[/tex]
The area of the sector is 8 square meters
