To find the total square footage (area) of a circular patio with a given radius, we can use the formula for the area of a circle:
[tex]\[
\text{Area} = \pi \times (\text{radius})^2
\][/tex]
Let's break this down step-by-step:
1. Identify the radius:
The radius of the patio is given as 20 feet.
2. Substitute the radius into the formula:
[tex]\(\text{Area} = \pi \times (20)^2\)[/tex]
3. Square the radius:
[tex]\(20^2 = 400\)[/tex]
4. Multiply by [tex]\(\pi\)[/tex]:
[tex]\(\text{Area} = \pi \times 400\)[/tex]
The value of [tex]\(\pi\)[/tex] (pi) is approximately 3.14159. So,
[tex]\[
\text{Area} \approx 3.14159 \times 400
\][/tex]
5. Perform the multiplication:
[tex]\[
\text{Area} \approx 3.14159 \times 400 = 1256.636
\][/tex]
Therefore, the total square footage of the patio is approximately 1256.64 square feet.
