Final answer:
The perimeter of the quarter circle can be approximated using the formula P = π * √(50.24) / 2, where π is a mathematical constant approximately equal to 3.14.
Step-by-step explanation:
The area of a quarter circle can be found using the formula A = (π * r^2)/4, where A is the area and r is the radius. In this case, the area is given as 12.56 square yards.
12.56 = (π * r^2)/4
Multiplying both sides of the equation by 4 and dividing by π, we get:
r^2 = (12.56 * 4) / π
r^2 = 50.24 / π
r ≈ √(50.24 / π)
Next, we can find the perimeter of the quarter circle using the formula P = 2πr/4, where P is the perimeter.
P = (2π * r)/4
Substituting the value of r we obtained:
P ≈ (2π * √(50.24 / π))/4
P ≈ (π * √(50.24 / π))/2
P ≈ (π * √(50.24) * √(1/π))/2
P ≈ π * √(50.24) / 2
Finally, we can approximate the value of P:
P ≈ 3.14 * √(50.24) / 2