## Explanation

Given the perimeter of a quarter circle is 3.57 cm, we need to find its area.

First, let's break down the components of the given perimeter. The perimeter $P$ of a quarter circle includes:

- One-fourth of the circle's circumference
- The two radii

If $r$ is the radius of the circle, the total perimeter of the quarter circle can be represented as:

$P = \frac{1}{4} \times 2\pi r + 2r$Given:

$P = 3.57 \, \text{cm}$We can write the equation as:

$\frac{1}{2} \pi r + 2r = 3.57$Now, let's solve for the radius $r$.

First, we'll combine the terms involving $r$:

$r \left( \frac{\pi}{2} + 2 \right) = 3.57$Solving for $r$:

$r = \frac{3.57}{\frac{\pi}{2} + 2}$ $r = \frac{3.57}{1.57 + 2}$ $r \approx \frac{3.57}{3.57} = 1 \, \text{cm}$So, the **radius** $r$ is approximately $1 \, \text{cm}$.

Next, we compute the **area** $A$ of the quarter circle. The area of a full circle is $\pi r^2$, so the area of a quarter circle is:

Using the radius we found:

$A = \frac{1}{4} \pi (1)^2$ $A = \frac{1}{4} \pi$Plugging in the value of $\pi \approx 3.14159$:

$A \approx \frac{3.14159}{4}$ $A \approx 0.7854 \, \text{cm}^2$Therefore, the **area of the quarter circle** is approximately **0.7854 cm$^2$**.