The area would be 247.8 sq. in.
We start out finding the length of the apothem. The apothem of a regular polygon is given by
[tex]A=\frac{s}{2\tan{(\frac{180}{n})}}[/tex]
where s is the side length and n is the number of sides. Using our information, we have
[tex]A=\frac{5}{2\tan{(\frac{180}{5})}}=\frac{5}{2\tan{36}}=8.26[/tex]
Now we find the area of the polygon using the formula:
A = n(1/2)(b)(h), where n is the number of sides, b is the side length, and h is the length of the apothem:
A = 5(1/2)(8.26)(12) = 247.8
