Quadrant

''For half a protractor, used in astronomy, see quadrant (astronomy). It is the shape of this.''

A quadrant is a sector of a circle, which is half a semicircle.

Measurements
The area of a quadrant is $${1\over4}\pi r^2$$, being $1/undefined$ of a circle.

Perimeter
The perimeter of a quadrant is $$(1+{1\over4}\pi) d$$, where d is the diameter of the circle, or twice the radius.

This can be easily explained by looking at how the quadrant looks.

The 2 straight sides in the quadrant are the radii and 2r = d.

The curve in the quadrant is a quarter of the circumference of the circle, making the length of the curve $${1\over4}\pi d$$.

When both are added up, they become equal to $$(1+{1\over4}\pi)d$$:

$$\begin{align}P&={\frac{1}{4}\pi d}+d\\&={\frac{1}{4}\pi d}+1d\\&=(\frac{1}{4}\pi + 1)d\end{align}$$

Length of arc
The arc in the quadrant is explained in the perimeter section. It is equal to $${1\over4}\pi d$$.

Angle measurement
The angle between the two radii is $&pi;⁄2$ radians or 90&deg;.