Cross

A cross is a shape made from two elongated parts that intersect, usually near their centers. In the most familiar version, the two parts meet at a right angle, creating a horizontal arm and a vertical arm. However, a cross does not have one single mathematical form: its arms can have different lengths and widths, and their arrangement may vary.

A simple cross can be drawn by combining two rectangles that overlap. Depending on its proportions, it may have several lines of symmetry. For example, a cross with four equal arms has both vertical and horizontal symmetry, and it also has rotational symmetry of order four: after a quarter turn, the shape looks unchanged.

Cross-shaped forms appear in many areas of everyday life. They can be used in signs, diagrams, maps, games, tools, construction and decorative designs. In geometry, the word “cross” generally describes a shape rather than a single precisely defined figure, so its properties depend on how it is constructed.

This makes it useful for observing basic ideas such as length, width, angles, symmetry and area. To find the area of a simple cross made from two overlapping rectangles, the area of the shared part must be counted only once. A cross can therefore be both an easy shape to recognize and a useful example for exploring how several simple geometric parts can form one larger figure.