Answer:
12,370.34 square yards
Explanation:
The shaded area between the two circles is known as an annulus.
This can be computed by the formula
A₂ - A₁
where
A₁ = area of the inner (smaller circle)
A₂ = area of the outer (larger circle)
We also have
A₁ = π · r₁²
A₂ = π · r₂²
where
r₁ = radius of inner circle
r₂ = radius of outer circle
So
Area of shaded region (area of annulus)
= π · r₂² - π · r₁²
= π (r₂² - r₁²)
We are given r₁ = 25.9 yds
Outer circle has a radius r₂ = inner circle radius + annulus width
r₂ = 25.9 + 42
r₂ = 67.9 yds
Area of the shaded region
= π (67.9² - 25.9²)
= π (4,610.41 - 670.81)
= π x 3,939.6
= 12,370.344 square yards (using π = 3.14)
= 12,370.34 square yards (rounded to nearest hundredth)