The diameter of a circle is a line segment having its endpoints on the circle and which contains the center of the circle. A diameter divides the circle into two arcs of equal length. Because the center divides a diameter is two line segments of equal length, that being the radius, \(r\) of the circle. It is well known that the area of the circle is \(\pi r^2\) square units. Also well is the the length of the circumference of the circle is \(\pi D=2\pi r\).
There are various ways you might prove this formally, depending on what theorems you have about congruent sectors, or something like that.