find the circumference and area of the figure if each unit on the graph measures 1 centimeter. round answers…

Explanation:

Step1: Calculate the radius

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the radius. Here, the center of the circle is $A(5,3)$ and a point on the circle is $B(2,1)$. $r=\sqrt{(5 - 2)^2+(3 - 1)^2}=\sqrt{3^2+2^2}=\sqrt{9 + 4}=\sqrt{13}\approx3.6$ cm.

Step2: Calculate the circumference

The formula for the circumference of a circle is $C = 2\pi r$. $C=2\pi\times\sqrt{13}\approx2\times3.14\times3.6\approx22.6$ cm.

Step3: Calculate the area

The formula for the area of a circle is $A=\pi r^{2}$. $A=\pi\times(\sqrt{13})^{2}=13\pi\approx13\times3.14 = 40.8$ cm².

Answer:

circumference = $22.6$ cm area = $40.8$ cm²