Find the area, perimeter, interior angle, and apothem of a regular polygon. Enter the number of sides and the side length.
Usage Tip
As the number of sides grows, a regular polygon approaches a circle — its area nears pi times the apothem squared.
area = (1 ÷ 2) × perimeter × apothem
The apothem is the distance from the center to the midpoint of a side; it acts like the height for the area.
Interior angles grow toward 180 degrees as sides increase.
The apothem depends on the side length and the number of sides.
A regular polygon has equal sides and equal angles. Each interior angle equals 180 times the number of sides minus 2, divided by the number of sides. The apothem is the distance from the center to the midpoint of a side, and the area equals half the perimeter times the apothem.
The apothem is useful for finding the area of shapes like hexagons and octagons by splitting them into identical triangles around the center. As the number of sides grows, the polygon looks more and more like a circle. Check that you enter at least three sides, since two sides do not enclose any area.