Question

Find the area of the rug. DO NOT ROUND.

what is the area?

Answer 1

28.26 ft²

Explanation:

Formula:

`\text{Area of circular rug:} = \pi r^(2)`

Determining the radius of the circular rug:

To determine the radius, we need to divide the diameter by 2.

Given diameter: 6 feet

`\implies {\frac{\text{Diameter}}{2} = \text{Radius}`

`\implies {\frac{\text{6}}{2} = \text{Radius}`

`\implies 3\ \text{feet} = \text{Radius}`

Replacing the radius in the formula:

`\implies \text{Area of circular rug:} = \pi (3)^(2)`

Determining the area of the circular rug:

`\implies \text{Area of circular rug:} = \pi (3)^(2)`

`\implies \text{Area of circular rug:} = 9\pi`

Replacing π as 3.14 (Approx. measure of π):

`\implies \text{Area of circular rug:} = 9(3.14)`

`\implies \text{Area of circular rug:} = 28.26 \ \text{ft}^(2)`

Answer 2

`(198)/(7) \ \text{feet}^(2)`

Explanation:

Given:

• Diameter of rug = 6 feet

To find the area of the rug, we need to use the formula "πr² or π(D/2)²"

Where:

• r = radius
• d = diameter

Since we do not have the radius, we need to substitute the diameter in the formula "π(D/2)²" to determine the area of the rug.

⇒
`\pi ((D)/(2) )^(2)`

⇒
`\pi ((6)/(2) )^(2)`

⇒
`\pi (3 )^(2)`

⇒
`\pi (3 )(3)`

⇒
`9\pi`

Substituting "22/7" as π:

⇒
`9((22)/(7) )`

⇒
`((198)/(7) )`

When finding the area of ANY shape, do not forget to include the units.

⇒
`(198)/(7) \ \text{feet}^(2)`