The Area of Polygon Segment from Number of Sides and Inner Radius calculator computes the area of one of n triangular segments of a regular polygon of n sides circumscribed around a circle of radius r. See the colored segment of the polygon shown in Figure 1.
INSTRUCTIONS: Choose units and enter the following:
Polygon Segment Area (A): The calculator returns the area in square meters. However, this can be automatically converted to compatible units via the pull-down menu.
A regular polygon is a geometric shape with three or more straight sides where every side is the same length and every angle between connecting sides are the same angle. Because of the symmetry of the regular polygon, all the vertices of the polygon can be constructed to touch a circle in which the regular polygon is inscribed and all the chords that are polygon sides will then obviously be of equal length . Likewise, because of the regular polygon's symmetry, a circle constructed to be inscribed in a regular polygon and touching the polygon will touch the regular polygon at the midpoint of the polygon side. As shown in the pictures, Figure 1 and Figure 2, lines from the regular polygon's vertices to the circle's center form n isosceles triangles of equal area.
The names of polygons vary based on the number of sides as follows:
Polygon Area Calculators:
Polygon Side Calculators
Polygon Perimeter Calculators
Other Polygon Calculators