Answer:
[tex]\boxed{\text{51.71 cm}^{2}}[/tex]
Step-by-step explanation:
If the angle θ is in radians, the formula for the area (A) of a sector of a circle is
A = ½r²θ
If θ is in degrees
[tex]A = \dfrac{1}{2}r^{2}\theta \times \dfrac{\pi \text{ rad}}{180^{\circ}}= \pi r^{2}\times\dfrac{\theta }{360}[/tex]
Data:
θ = 49°
r = 11 cm
Calculation:
[tex]\begin{array}{rcl}A& = &3.14\times 11^{2}\times\dfrac{49}{360}\\\\ & = &3.14 \times 121 \times 0.1361\\ & = & \mathbf{51.71}\\\end{array}\\\text{The area of the sector is }\boxed{\textbf{51.71 cm}^{2}}[/tex]
