The amount of fence needed is the perimeter of the fence. The amount of fence needed is 127.1ft
From the diagram of the fence, we have:
[tex]r = 15[/tex] ---- the radius
[tex]l = 40ft[/tex] -- the length of the parallel lines
First, we calculate the length of the arc surrounding the half circle
This is calculated using:
[tex]L = \frac{\theta}{360} \times 2\pi r[/tex]
Because it is a half circle
[tex]\theta = 180[/tex]
So, we have:
[tex]L = \frac{\180}{360} \times 2 \times 3.142 \times 15[/tex]
[tex]L =0.5 \times 2 \times 3.142 \times 15[/tex]
[tex]L =47.13[/tex]
The amount of fence needed is the sum of the length of parallel lines and the semicircle.
So, we have:
[tex]Amount = L + l + l[/tex]
[tex]Amount =47.13 + 40 + 40[/tex]
[tex]Amount =127.13[/tex]
Approximate
[tex]Amount =127.1[/tex]
Hence, the amount of fence needed is 127.1ft
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