Question

Find the perimeter of each of these sectors. (Give your answers in terms of $\mathrm{\pi }$)

Answer 1

Given:
Central angle, $\mathrm{\theta }$ = 40$°$
Radius of the circle = 8 cm
Now,
Length of the arc, l = $\frac{\theta }{360}\times 2\mathrm{\pi }r$

= $\frac{40}{360}\times 2\times \mathrm{\pi }\times 8\mathrm{cm}$

= $\frac{16}{9}\mathrm{\pi }$

Thus, we have:
Perimeter of the sector = Length of the arc (l) of the circle + 2(Radius of the circle)
= $\left(\frac{16}{9}\mathrm{\pi }+16\right)$ cm