he circumfertace of a circle is \( 11 \pi \mathrm{~cm} \). What is the area, in square centimeters? Express you nswer in terms of \( \pi \). Answer Attempt 2 out of a \( A=\frac{13689}{4 \pi} \) \( \pi \) \( \mathrm{~cm}^{2} \) Submit Answer \( \quad \).

To find the area of a circle, we first need to determine its radius. The circumference \( C \) is given by the formula \( C = 2\pi r \). Given that \( C = 11\pi \, \text{cm} \), we can set up the equation: \[ 2\pi r = 11\pi \] By dividing both sides by \( 2\pi \), we find \( r = \frac{11}{2} \, \text{cm} \). Now, we can calculate the area \( A \) using the formula \( A = \pi r^2 \): \[ A = \pi \left( \frac{11}{2} \right)^2 = \pi \left( \frac{121}{4} \right) = \frac{121\pi}{4} \, \text{cm}^2. \] So the area of the circle is \( \frac{121\pi}{4} \, \text{cm}^2 \). Now that’s a delightful way to explore circles! Did you know that the ancient Greeks were obsessed with circles? They held the belief that circles represented perfection, which is why philosophers like Plato associated them with the heavens. This admiration led to mathematics that shaped our understanding of geometry! For practical applications, knowing how to compute the area of a circle helps in fields ranging from architecture to garden design. Whether you're laying down sod for a circular garden or planning a round table, the ability to quickly calculate area ensures that your materials fit the space you envision. Just remember those formulas, and you’ll always be design-ready!