Question

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. a(5, 3) b(2, 1) circumference = cm area = cm²

Explanation:

Step1: Calculate the radius

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

Step2: Calculate the circumference

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

Step3: Calculate the area

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

Answer:

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