Question

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

Answer 1

`"Area" = 30 " sq.ft."`

Explanation:

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.