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* (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* (6\cdot 8)/(2) = 7 * 6\cdot 4 = 168`