To obtain the area of the sector, the following steps are necessary:
Step 1: Recall the general formula of the area of a sector, as follows
[tex]A_{sector}=\frac{\theta}{360}\times\pi\times r^2[/tex]
Where:
[tex]\begin{gathered} \theta=angle\text{ of the sector's arc} \\ r=\text{radius of the circle} \\ \pi=\text{ 3.142} \end{gathered}[/tex]
Step 2: Apply the formula to the question at hand, as follows:
[tex]\begin{gathered} A_{sector}=\frac{\theta}{360}\times\pi\times r^2 \\ \text{where: }\theta=45^o,\text{ r= 10cm} \\ \text{Thus:} \\ A_{sector}=\frac{45}{360}\times\pi\times10^2 \\ \Rightarrow A_{sector}=\frac{45}{360}\times\pi\times100=\frac{4500}{360}\times\pi \\ \Rightarrow A_{sector}=12.5\times\pi=12.5\pi cm^2 \end{gathered}[/tex]
Therefore, in its simplest form, the area of the sector is 12.5π square centimeters
