So a area of a polygon is the perimeter * the apothem divided by 2
[tex]\frac{P*a}{2} = A[/tex]
So lets find the perimeter first.
P = sn, where s is the length of a side and n is the number of sides
P = (12)(5) = 60
Now on to the apothem.
[tex]a = \frac{s}{2tan(\frac{180}{n}) }[/tex] s and n represent the same things as before
[tex]a = \frac{12}{2tan(\frac{180}{5}) }[/tex]
That is approximately 8.258
Now that we have both the perimeter and the apothem, we can solve for the area.
[tex]A=\frac{60*8.258}{2}[/tex]
A = 247.74
247.74 rounded to the nearest tenth is 247.7 making the answer
247.7 squared ft
