Respuesta :

Answer:

329.9 ft^2

Step-by-step explanation:

area = π · r^2

diameter = 2r so radius = 10.25

area = 3.14 · 10.25^2

10.25^2 = 105.06

3.14 · 105.06 = 329.9 ft^2

Given :-

  • diameter = 20.5 ft
  • π = 3.14

[tex] \\ \\ [/tex]

To find :-

  • Area

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Solution:

To find area first we should know value of radius.

Diameter is given , and from diameter we can find value of radius.

[tex] \\ [/tex]

We know :-

[tex] \bf \ddag\boxed{\rm Diameter =2 \: radius } \bf \ddag[/tex]

By using this formula we can find radius.

[tex] \\ \\ [/tex]

[tex] \hookrightarrow\sf Diameter =2 \: radius [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf 20.5 =2 \: radius [/tex]

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[tex] \hookrightarrow\sf \dfrac{205}{10} =2 \: radius [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf \cancel\dfrac{205}{10} =2 \: radius [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf \dfrac{41}{2} =2 \: radius [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf2 \: radius = \dfrac{41}{2} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf \: radius = \dfrac{41}{2 \times 2} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf \: radius = \dfrac{41}{4} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\bf \: radius = 10.25[/tex]

[tex] \\ \\ [/tex]

Now let's find Area

we know :-

[tex] \bf \ddag\boxed{\rm Area = \pi radius {}^{2} } \bf \ddag[/tex]

[tex] \\ \\ [/tex]

So:-

[tex] \\ [/tex]

[tex] \dashrightarrow \sf Area = \pi radius {}^{2} [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf Area = \pi (10.5) {}^{2} [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf Area = \pi \times 10.5 \times 10.5 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf Area = \pi \times 110.25 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf Area = 3.14 \times 110.25 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \bf Area =346.19~ {ft}^{2} \{approx\}\\[/tex]

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