Question

Find the area of a regular polygon with 7 sides that has a side length of 6 inches and an apothem of 8 inches

Answer 1

We can always split a regular polygon with $n$ sides into $n$ triangles, whose base is the side of the polygon and whose height is the apothem of the polygon. So, the sum of the areas of all these triangles is

$A=n\times \dfrac{s\cdot a}{2}$

where $n$ is the number of sides, $s$ is the side length, and $a$ is the apothem length.

So, you just need to plug you values in: in your case, you have $n=7,\ s=6,\ a=8$

So, the formula becomes

$A=7\times \dfrac{6\cdot 8}{2} = 7 \times 6\cdot 4 = 168$