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fieryanswererft

Answer:

28.26 ft²

Explanation:

[tex]\sf area \ of \ circle = \pi r^2[/tex]

Here given diameter: 6 ft

radius: d/2 = 6/2 = 3 ft

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area of rug:

[tex]\dashrightarrow \ \pi (3)^2[/tex]

[tex]\dashrightarrow \ 9\pi[/tex]

[tex]\dashrightarrow \ 9(3.14)[/tex]

[tex]\dashrightarrow \ 28.26 \ ft^2[/tex]

Answer:

[tex]\underline{\underline{28.26 \ \text{feet}^{2}}}[/tex]

Step-by-step explanation:

Step-1) Determine the radius of the rug:

Given diameter: 6 feet

  • ⇒ [tex]\text{Diameter = 2(Radius)}[/tex]
  • ⇒ [tex]\frac{\text{Diameter}}{2} = \frac{\text{Radius}}{2}[/tex]
  • ⇒ [tex]\frac{\text{Diameter}}{2} = \text{Radius}[/tex]

Substitute the diameter to obtain the radius of the rug.

  • ⇒ [tex]\frac{6}{2} = \text{Radius}[/tex]
  • ⇒ [tex]\text{3 feet = Radius}[/tex]

Step-2) Find the area of the rug by substituting the radius in the formula:

Area of circular rug  = πr²

                                  = [tex]\pi (3)^{2}[/tex]

                                  = [tex]\pi (3)(3)[/tex]

                                  = [tex]\pi(9)[/tex]

Substituting π as 3.14 (Stated in comments):

                                  = [tex](3.14)9[/tex]

                                  = [tex]\underline{\underline{28.26 \ \text{feet}^{2}}}[/tex]

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