Answer:
[tex] \boxed{Perimeter \: of \: semicircle = 61.68 \: feet} [/tex]
Given:
[tex] \sf Area \: of \: semicircle = 226.08 \: square \: feet[/tex]
To find:
Perimeter of semicircle
Step-by-step explanation:
Let 'r' be the radius of circle
[tex] \sf \implies Area \: of \: semicircle = \frac{ \pi {r}^{2} }{2} \\ \\ \sf \implies 226 .08 = \frac{\pi {r}^{2} }{2} \\ \\ \sf \implies \frac{\pi {r}^{2} }{2} = 226.08 \\ \\ \sf \implies \pi {r}^{2} = 2 \times 226.08 \\ \\ \sf \implies \pi {r}^{2} = 452.16 \\ \\ \sf \implies 3.14 \times {r}^{2} = 452.16 \\ \\ \sf \implies {r}^{2} = \frac{452.16}{3.14} \\ \\ \sf \implies {r}^{2} = 144 \\ \\ \sf \implies {r}^{2} = {12}^{2} \\ \\ \sf \implies \sqrt{ {r}^{2} } = \sqrt{ {12}^{2} } \\ \\ \sf \implies r = 2 \: feet[/tex]
So,
[tex] \sf Perimeter \: of \: semicircle = \pi r + 2r \\ \\ \sf =( 3.14 \times 12) +( 2 \times 12)\\ \\ \sf = 37.68 + 24 \\ \\ \sf = 61.68 \:ft[/tex]
