Question

How do I I find the area when I’m only given the apothem. How would I solve? The given polygon is square.

Answer 1

In triangle ONA,

`\begin{gathered} \sin 45=(NA)/(OA) \\ NA=OA\sin 45 \\ NA=8\sin 45 \\ NA=5.65 \end{gathered}`

Thus the value of a and s can be determined as,

`\begin{gathered} a=2NA \\ a=2*5.65\text{ m} \\ a=11.3\text{ m} \\ s=a \\ =11.3\text{ m} \end{gathered}`

The perimeter and area can be determined as,

`\begin{gathered} P=4a \\ P=4*11.3\text{ m} \\ P=45.2\text{ m} \\ A=a^2 \\ =(11.3m)^2 \\ =127.69m^2 \end{gathered}`

Thus, the required perimeter is 45.2 m and required area is 127.69 square meters.