PLEASE HELP! Daniela has a rectangular yard with a pool in the shape of a semicircle. How many square feet of grass does Daniela need to cover her yard, but not the pool?

Accepted Solution

Answer:Part 1) Area of rectangle [tex]3,600\ ft^{2}[/tex]Part 2) Area of semicircle [tex]1,413\ ft^{2}[/tex]Par 3) Total area of grass [tex]2,187\ ft^{2}[/tex]Step-by-step explanation:we know thatThe total area of grass is equal to the area of rectangle minus the area of semicirclestep 1Find the area of rectangleThe area of rectangle is equal to[tex]A=45*80=3,600\ ft^{2}[/tex]step 2Find the area of semicircleThe area of semicircle is equal to[tex]A=\frac{1}{2}\pi r^{2}[/tex]we have[tex]r=60/2=30\ ft[/tex] -----> the radius is half the diametersubstitute[tex]A=\frac{1}{2}(3.14)(30)^{2}[/tex][tex]A=1,413\ ft^{2}[/tex]step 3Find the total area of grass[tex]3,600\ ft^{2}-1,413\ ft^{2}=2,187\ ft^{2}[/tex]