Question

radius of a sector of a circle is 21 CM in length of an Arc of that sector is 55 cm find the find the area of the sector

Answer 1

area of the sector = 577.5

Answer 2

Here arc AB = 55 cm
AO= r= 21 cm
arc AB =
$2\pi \times r \times \frac{ \alpha }{360} \\ 55 = 2\pi \times 21 \times \frac{ \alpha }{360} \\ \alpha = 150$
Now area of sector =
$\frac{ \alpha }{360} \times \pi \times {r}^{2} \\ \frac{150}{360} \times \pi \times {21}^{2} \\ = 577.5$
Area of sector is 577.5 cm^ 2