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. circumference: cm area: cm²

Explanation:

Step1: Find the radius

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) to find the distance between \(A(2,3)\) and \(B(4,1)\).
\(r=\sqrt{(4 - 2)^2+(1 - 3)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx2.8\)

Step2: Calculate the circumference

The formula for the circumference of a circle is \(C = 2\pi r\).
\(C=2\pi\times2\sqrt{2}\approx2\times3.14\times2.8 = 17.6\)

Step3: Calculate the area

The formula for the area of a circle is \(A=\pi r^{2}\).
\(A=\pi\times(2\sqrt{2})^{2}=\pi\times8\approx3.14\times8 = 25.1\)

Answer:

circumference: \(17.6\) cm
area: \(25.1\) \(cm^{2}\)