# Sector area

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The sector area is the measure of the area along the curved line filling up the arc sector. It is longer than the straight line distance between its endpoints (which would be a chord) The formula the arc measure is:

$\frac{\theta}{360}R^2\pi$

where:

$\theta$ is the central angle of the arc in degrees
R is the radius of the arc

Recall that $R^2\pi$ is the area of the whole circle, so the formula simply reduces this by the ratio of the arc angle to a full angle (360). By transposing the above formula, you solve for the radius, central angle, or secto area if you know any two of them.

The sector area of a Polygon is:

$\frac{\theta}{180n-360}A_n$

## Circumscribed sector area

The sector area of a circumscribed circle is:

$\frac{\theta}{360} s^2\frac{\pi}{4sin^2(\frac{180}{n})}$

## Inscribed sector area

The sector area of a inscribed circle is:

$\frac{\theta}{360} s^2\frac{\pi}{4tan^2(\frac{180}{n})}$