Shape (Geometry)

A shape is the outline or form of an object. In geometry, the part of math that studies shapes, a shape is described by its sides, angles, and curves. Shapes are everywhere. The wheel of a bike is a circle. A door is a rectangle. A slice of pizza is a triangle. Geometry gives us a way to talk about all of them with the same set of rules.

Shapes come in two main groups. Flat shapes are called two-dimensional, or 2D. They have length and width, but no thickness. A square drawn on paper is 2D. Solid shapes are called three-dimensional, or 3D. They have length, width, and depth, so you can hold them. A cube, like a die, is 3D. Every 3D shape is built out of 2D shapes joined together. A cube has six square faces. A pyramid has a square bottom and four triangle sides.

Flat shapes with straight sides are called polygons. The name of a polygon comes from how many sides it has. A triangle has three sides. A quadrilateral has four. A pentagon has five, a hexagon six, an octagon eight. The word "polygon" comes from Greek and means "many corners." A circle is not a polygon, because it has no straight sides at all. It is one smooth curve.

Shapes can be sorted by their angles too. A right angle is a perfect square corner, like the corner of a book. Shapes with all right angles, like squares and rectangles, fit together neatly. Shapes with sharper or wider angles do not. This is why floors are tiled with squares or hexagons but almost never with pentagons. Pentagons leave gaps.

Some shapes have symmetry, which means one half matches the other half. If you fold a square in half, the two sides line up perfectly. A circle has even more symmetry. You can fold it through its center in any direction and the two halves always match.

Shapes are not just for math class. Engineers use triangles in bridges because triangles are the strongest shape. A triangle cannot be pushed out of its form without bending its sides. Squares and rectangles can wobble. That is why you see triangle braces inside the metal frames of bridges, towers, and roofs. The shape itself is doing the work of holding things up.