find the circumference and area of the figure if each unit on the graph measures 1 centimeter. round answers to the nearest tenth, if necessary.
circumference
cm
area
cm²

Question

Accepted Answer

# Explanation:
## Step1: Find the radius
The center of the circle is $ A(2, 3) $ and a point on the circle is $ B(4, 1) $. Using the distance formula $ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $, the radius $ r $ is the distance between $ A $ and $ B $.
$$
\begin{align*}
r&=\sqrt{(4 - 2)^2 + (1 - 3)^2}\
&=\sqrt{2^2 + (-2)^2}\
&=\sqrt{4 + 4}\
&=\sqrt{8}\
&=2\sqrt{2}\approx 2.8 \text{ cm}
\end{align*}
$$
## Step2: Calculate the circumference
The formula for the circumference of a circle is $ C = 2\pi r $. Substituting $ r = 2\sqrt{2} $:
$$
\begin{align*}
C&=2\pi\times2\sqrt{2}\
&=4\sqrt{2}\pi\
&\approx 4\times1.414\times3.14\
&\approx 17.7 \text{ cm}
\end{align*}
$$
## Step3: Calculate the area
The formula for the area of a circle is $ A = \pi r^2 $. Substituting $ r = 2\sqrt{2} $:
$$
\begin{align*}
A&=\pi\times(2\sqrt{2})^2\
&=\pi\times8\
&=8\pi\
&\approx 25.1 \text{ cm}^2
\end{align*}
$$
# Answer:
Circumference: $\approx 17.7$ cm, Area: $\approx 25.1$ $ \text{cm}^2 $

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QUESTION IMAGE

Question

Explanation:

Step1: Find the radius

Step2: Calculate the circumference

Step3: Calculate the area

Answer: