To work out the length of an arc, we use the following equation:
[tex]arclength=\frac{angle}{360}\times 2\pi r[/tex] (r stands for radius)
So just substitute in the values to get the arc length of the first sector:
(angle = 40, radius = 12)
[tex]arclength=\frac{angle}{360}\times 2\pi r[/tex]
[tex]arclength=\frac{40}{360}\times 2\pi 12[/tex]
[tex]arclength = \frac{8}{3} \pi[/tex]
For the other sector, the angle will also be 40, since opposite angles are the same. So to get the arc length, we substitute in:
(angle = 40, radius = 5)
[tex]arclength=\frac{angle}{360}\times 2\pi r[/tex]
[tex]arclength=\frac{40}{360}\times 2\pi 5[/tex]
[tex]arclength=\frac{10}{9}\pi[/tex]
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Now to get the perimeter, we add up all of the arc lengths and side lengths:
[tex]Perimeter =\frac{8}{3}\pi+\frac{10}{9}\pi + 12 + 12 + 5 + 5[/tex]
[tex]Perimeter = \frac{34}{9}\pi +34[/tex]
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Answer:
Perimeter = [tex]\frac{34}{9}\pi +34[/tex]cm or 45.87cm rounded to 2 decimal places.
