In triangle ONA,
[tex]\begin{gathered} \sin 45=\frac{NA}{OA} \\ NA=OA\sin 45 \\ NA=8\sin 45 \\ NA=5.65 \end{gathered}[/tex]
Thus the value of a and s can be determined as,
[tex]\begin{gathered} a=2NA \\ a=2\times5.65\text{ m} \\ a=11.3\text{ m} \\ s=a \\ =11.3\text{ m} \end{gathered}[/tex]
The perimeter and area can be determined as,
[tex]\begin{gathered} P=4a \\ P=4\times11.3\text{ m} \\ P=45.2\text{ m} \\ A=a^2 \\ =(11.3m)^2 \\ =127.69m^2 \end{gathered}[/tex]
Thus, the required perimeter is 45.2 m and required area is 127.69 square meters.
