Respuesta :

Intriguing456

Answer:

[tex]A_\text{sector} = \dfrac{49}{9}\pi\text{ units}^2\\\\ \text{ } \ \ \ \ \ \ \ \,\approx 17.1\text{ units}^2[/tex]

Step-by-step explanation:

We can find the area of the sector using the equation:

[tex]A_\text{sector} = \dfrac{\theta}{360\°} \cdot A_\text{circle}[/tex]

where:

  • [tex]\theta[/tex] = central angle of the sector

We can also substitute in the area of a circle formula to get:

[tex]A_\text{sector} = \dfrac{\theta}{360\°} \cdot \pi r^2[/tex]

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Notice that the number:

[tex]\dfrac{\theta}{360\°}[/tex]

tells us what fraction of the circle's total area that the sector takes up.

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We are given the following information:

  • [tex]\theta = \overset{\frown}{AB} = 40\°[/tex]
  • [tex]r = BC = 7[/tex]

Plugging these into the sector area equation, we get:

[tex]A_\text{sector} = \dfrac{40\°}{360\°} \cdot \pi(7^2)[/tex]

[tex]A_\text{sector} = \dfrac{1}{9} \cdot 49\pi[/tex]

[tex]A_\text{sector} =\boxed{ \dfrac{49}{9}\pi\text{ units}^2}\\\\ \text{ } \ \ \ \ \ \ \ \,\approx \boxed{17.1\text{ units}^2}[/tex]

msm555

Answer:

[tex] \dfrac{49\pi}{9} [/tex]

Step-by-step explanation:

To find the area of the sector, we'll use the formula for the area of a sector of a circle:

[tex] \Large\boxed{\boxed{\textsf{Area} = \dfrac{\theta}{360^\circ} \times \pi r^2}} [/tex]

Where:

  • θ is the central angle of the sector in degrees,
  • r is the radius of the circle.

Given:

  • θ (arc AB)= 40° (central angle),
  • r (BC)= 7 units.

Substitute the value:

[tex] \textsf{Area} = \dfrac{40^\circ}{360^\circ} \times \pi (7)^2 [/tex]

[tex] \textsf{Area} = \dfrac{1}{9} \times 49\pi [/tex]

[tex] \textsf{Area} = \dfrac{49\pi}{9} [/tex]

So, the expression for the area of the sector is:

[tex] \dfrac{49\pi}{9} \textsf{units}^2[/tex]

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