Explanation:
the area of the full larger circle minus the area of the smaller circle.
the area of a circle is
pi×r²
the radius of the smaller circle is 23.1 yd.
the radius or the larger circle is 23.1 + 7.8 = 30.9 yd.
the area of the larger circle is
pi×30.9² = 3.14 × 954.81 = 2,998.1034 yd²
the area of the smaller circle is
pi× 23.1² = 1,675.5354 yd²
the area of only the ring around the smaller circle is then
2,998.1034 - 1,675.5354 = 1,322.568 yd² ≈
≈ 1,322.57 yd²
or
pi×30.9² - pi×23.1² = pi(954.81 - 533.61) =
= 421.2pi = 421.2 × 3.14 =
= 1,322.568 ≈ 1,322.57 yd²