What would be the area of a regular polygon with a perimeter of 20 feet and an apothem of 3 feet?

##"Area" = 30 " sq.ft."##

A regular polygon with ##n## sides can be divided into ##n## sub-triangles each with its center at the center of the polygon. Given ##color(white)("XXX")##An apothem of ##3## feet and ##color(white)("XXX")##a polygon perimeter of ##20## feet.

Each triangle will have an area of ##color(white)("XXX")(3xx20/n)/2 ##(sq.ft.)

and since there are ##n## of these triangles the total area of the polygon will be ##color(white)("XXX")nxx[(3xx20/n)/2]## (sq.ft.)

##color(white)("XXX")=cancel(n)xx[(3xx(cancel(20)^10)/cancel(n))/cancel(2)]## (sq.ft.)

##color(white)("XXX")=30## sq.ft.