A family room has a circular rug with a radius of 2 meters. What is the rug's area?

1. ### Break Down the Problem

To find the area of a circular rug, we need to use the formula for the area of a circle. The formula is given by: $A = \pi r^2$ where $A$ is the area, and $r$ is the radius.

2. ### Relevant Concepts

The radius of the circular rug is given as $2$ meters. We will substitute this value into the formula to calculate the area.

3. ### Analysis and Detail

Let's perform the calculation step-by-step:

1. Identify the radius:
   $r = 2 \, \text{meters}$

2. Substitute the radius into the area formula: $A = \pi (2)^2$

3. Calculate $(2)^2$: $(2)^2 = 4$

4. Therefore, the area becomes: $A = \pi \times 4$

5. Finally, we can approximate $\pi \approx 3.14$ for the calculation: $A \approx 3.14 \times 4 = 12.56 \, \text{square meters}$

4. ### Verify and Summarize

We verified the calculations, ensuring all steps followed the correct formula for the area of a circle. The final calculation approximated the numerical value of $\pi$.

Final Answer

The area of the circular rug is approximately $12.56$ square meters.