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.