A community pool that is shaped like a regular pentagon needs a new cover for the winter months. The radius of the pool is 20.10 ft. The pool is 23.62 ft on each side. To the nearest square foot, the area of the pool that needs to be covered is ft2.

Answer:[tex]960.42\text{ ft}^2[/tex] Step-by-step explanation:Please find the attachment.  We have been given that a community pool that is shaped like a regular pentagon needs a new cover for the winter months.To find the area of community pool we will use area of pentagon formula.[tex]\text{Area of pentagon}=\frac{1}{2}a*p[/tex], where, a represents the apothem or perpendicular distance from the center of the pentagon and p represents perimeter of pentagon. Let us find the perimeter of our given pentagon by multiplying each side length by 5.[tex]\text{Perimeter of community pool}=5\times 23.62[/tex][tex]\text{Perimeter of community pool}=118.1[/tex] Now let us find apothem of our pentagon by using Pythagoras theorem.  [tex]a^2=20.10^2-11.81^2[/tex][tex]a^2=404.01-139.4761[/tex][tex]a^2=264.5339[/tex][tex]a=\sqrt{264.5339}[/tex][tex]a=16.2645[/tex]Upon substituting our given values in above formula we will get, [tex]\text{Area of community pool}=\frac{1}{2}\times 16.2645\times 118.1[/tex][tex]\text{Area of community pool}=8.13224907\times 118.1[/tex][tex]\text{Area of community pool}=960.418615627971\approx 960.42[/tex]Therefore, the area of the pool that needs to be covered is 960.42 square feet.