Answer
$A=5a^2tan(36)$
Work Step by Step
We draw an apothem. Then, we draw a triangle that extends to a corner of the pentagon closest to the apothem. This means the angle created is:
$360/10=36$
We will call the apothem a. If we call the side that runs along the side of the pentagon b, we can find:
$tan(36)=b/a$
This means
$b=atan(36)$
From this, we find that the area of the triangle is:
$A=.5bh=.5a(atan(36))$
$A=.5a^2tan(36)$
Since there are 10 of these triangles within the pentagon, the total area is:
$A=5a^2tan(36)$
