Respuesta :

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=1.4\\ \theta = \frac{2\pi }{3} \end{cases}\implies A=\cfrac{\frac{2\pi }{3}\cdot 1.4^2}{2} \\\\\\ A=\cfrac{\frac{2\cdot 1.4^2\cdot \pi }{3}}{\frac{2}{1}}\implies A=\cfrac{2\cdot 1.4^2\cdot \pi }{3}\cdot \cfrac{1}{2}\implies A=\cfrac{1.96\pi }{3}[/tex]
MrRoyal

The area of the sector is 2.05 units

How to determine the sector area?

The radius is given as:

r = 1.4

The central angle is:

Angle = 2π/3

The area of the sector is calculated as:

[tex]Area = (\frac{\theta}{2}) * r^2[/tex]

So, we have:

[tex]Area = (\frac{2\pi}{3 * 2}) * 1.4^2[/tex]

Evaluate

Area  = 2.05

Hence, the area of the sector is 2.05

Read more about sector area at:

https://brainly.com/question/16736105

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