Plane Areas

This page provides formulas for the plane areas of geometric shapes.

Polygon

A shape formed by non-intersecting straight lines.

The area can be computed by dividing the shape into triangles and summing their areas.

Square

A rectangle with all sides equal.

Area = Side ^ 2

Area = (Diagonal ^ 2) / 2

Rectangle

A 4 sided polygon with all angles 90 degrees.

Area = Side1 * Side2

Parallelogram

A four sided polygon with opposite sides having equal length.

Area = Base * Height

Right Triangle

A triangle with one 90 degree angle.

Area = Leg1 * Leg2 / 2

Triangle

A three sided polygon.

Area = Base * Height / 2

Trapezoid

A four sided polygon with two sides parallel. 

Area = (ParallelLine1 + ParallelLine2) * Height / 2

Trapezium

A 4 sided polygon.

The areas can be computed by dividing the shape into two triangles and summing the triangle areas.

Regular Hexagon

A six sided regular polygon.

Area = 4.828 * (Side ^ 2)

Regular Polygon

A polygon with all angles equal and all sides equal.

MinorRadius = SQRT ((MajorRadius ^ 2) - ((Side ^ 2) / 4))
Area = NumberSides * Side * MinorRadius / 2

Circle

The locus of all points equidistant from a fixed point.

Area = Pi * (Radius ^ 2)

Circular Sector

A pie-shaped portion of a circle.

ArcLength = Radius * AngleDegrees * Pi / 180
Area = Radius * ArcLength / 2

Ellipse

The locus of points having a constant sum of distances to two fixed points.

Radius1 = distance from center of gravity to nearest edge point
Radius2 = distance from center of gravity to farthest edge point
Area = Pi * Radius1 * Radius2