<u>Given</u>:
Given that the regular decagon has sides that are 8 cm long.
We need to determine the area of the regular decagon.
<u>Area of the regular decagon:</u>
The area of the regular decagon can be determined using the formula,
![A=\frac{s^{2} n}{4 \tan \left(\frac{180}{n}\right)}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7Bs%5E%7B2%7D%20n%7D%7B4%20%5Ctan%20%5Cleft%28%5Cfrac%7B180%7D%7Bn%7D%5Cright%29%7D)
where s is the length of the side and n is the number of sides.
Substituting s = 8 and n = 10, we get;
![A=\frac{8^{2} \times 10}{4 \tan \left(\frac{180}{10}\right)}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B8%5E%7B2%7D%20%5Ctimes%2010%7D%7B4%20%5Ctan%20%5Cleft%28%5Cfrac%7B180%7D%7B10%7D%5Cright%29%7D)
Simplifying, we get;
![A=\frac{64 \times 10}{4 (\tan \ 18)}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B64%20%5Ctimes%2010%7D%7B4%20%28%5Ctan%20%5C%2018%29%7D)
![A=\frac{640}{4 (0.325)}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B640%7D%7B4%20%280.325%29%7D)
![A=\frac{640}{1.3}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B640%7D%7B1.3%7D)
![A=642.3](https://tex.z-dn.net/?f=A%3D642.3)
Rounding off to the nearest whole number, we get;
![A=642 \ cm^2](https://tex.z-dn.net/?f=A%3D642%20%5C%20cm%5E2)
Thus, the area of the regular decagon is 642 cm²
Hence, Option B is the correct answer.