Question

Find the area and perimeter of the following sector :

Radius= 4.2 cm, angle at the centre is 60 ° 

Answer 1

Area of the sector = ${\displaystyle (\pi {\text{r}}^2\times \frac{\theta }{{360}^{\circ }})}$

${\displaystyle =\frac{22}{7}\times 4.2\times 4.2\times \frac{{60}^{\circ }}{{360}^{\circ }}}$

= 9.24 cm²

Peri meter of the sector

= 2r + ${\displaystyle (2\pi \text{r}\times \frac{\theta }{{360}^{\circ }})}$

${\displaystyle =2\times 4.2+(2\times \frac{22}{7}\times 4.2\times \frac{{60}^{\circ }}{{360}^{\circ }})}$

= 8.4 + 4.4

 = 12.8 cm

Area of the sector = 9.24 cm² and perimeter = 12.8 cm