Question

Mrs. Hellerud bought 18.84 feet of fencing to go around her tree in her front yard. She wants to know the area to find how big of a bag of mulch she needs to buy to fill the space between the tree and fence. What is the area?

Answer 1

the fencing is the perimeter to the tree, then we can use the formula of the perimeter of a circle to replace this value

$\begin{gathered} P=2\times\pi\times r \\ 18.84=2\times\pi\times r \end{gathered}$

now we can solve r from the formula to know the radious

$\frac{18.84}{2\times\pi}=r$

we can use 3.14 to pi

$\begin{gathered} r=\frac{18.84}{2\times3.14} \\ \\ r=3 \end{gathered}$

the value of the radio is 3 feet

now we can use the formula of the area of the circle to calculate the total area

$A=\pi\times r^2$

and replace the known value of the radious and pi

$\begin{gathered} A=3.14\times3^2 \\ \\ A=28.26 \end{gathered}$

the area is 28.26 square feet