# Area

The physical amount of two-dimensional space that a shape takes up.

## Formulas

The area of a circle is given by one-half multiplied by τ (tau) multiplied by the radius of the circle squared.

The Area of a rectangle is given by its width multiplied by its height.

The area of a triangle is given by one-half multiplied by its width and height.

The area of any parallelogram is equal to the base multiplied by the height.

The area of a trapezoid is given by its height multiplied by the sum of its top length and bottom length divided by two.

The area between two vectors in 2D is given by the magnitude of their cross product. This formula is a generic way to find the area of any triangle given three points.