Answer:
[tex]A = 11.465\ m^2[/tex]
Step-by-step explanation:
Given
[tex]Fencing = 12\ m[/tex]
Required
Determine the area of the pen
The given parameter represents the perimeter of the pen;
Since, the pen is circular, we have circumference, C:
[tex]C = 2\pi r[/tex]
Substitute 12 for C
[tex]12 = 2\pi r[/tex]
Divide through by 2
[tex]6 = \pi r[/tex]
Make r the subject of formula
[tex]r = \frac{6}{\pi}[/tex]
The area (A) of the pen is calculated as follows;
[tex]A = \pi * r^2[/tex]
Substitute [tex]\frac{6}{\pi}[/tex] for r
[tex]A = \pi * (\frac{6}{\pi})^2[/tex]
Open Bracket
[tex]A = \pi * \frac{36}{\pi^2}[/tex]
[tex]A = \frac{36}{\pi}[/tex]
Take [tex]\pi[/tex] as 3.14
[tex]A = \frac{36}{3.14}[/tex]
[tex]A = 11.465\ m^2[/tex] (Approximated)
