2D and 3D Shapes: Names, Properties and Examples

A shape describes the outline or form of an object. Some shapes are flat, while others have length, width and height. Learning to identify shapes helps us understand geometry, measurement, design and the objects around us.

What are two-dimensional shapes?

A two-dimensional, or 2D, shape is flat. It has length and width but no thickness. We can draw it on paper. A triangle, rectangle and circle are common 2D shapes.

Important words used with shapes

Side

A side is a straight line segment that forms part of a flat shape. A triangle has three sides and a rectangle has four sides.

Vertex

A vertex is a corner where two sides meet. The plural of vertex is vertices. A square has four vertices.

Angle

An angle is formed when two rays or line segments meet. Angles are measured in degrees. A right angle measures exactly 90°.

Diagonal

A diagonal joins two non-adjacent vertices of a polygon. A rectangle has two diagonals.

Polygons

A polygon is a closed 2D shape made only from straight line segments. Its sides meet at vertices and do not leave a gap. A circle is not a polygon because its boundary is curved.

Triangle

A triangle has 3 sides, 3 vertices and 3 interior angles. The sum of its interior angles is 180°. Triangles can be classified by their sides or angles.

Quadrilateral

A quadrilateral has 4 sides, 4 vertices and 4 interior angles. The sum of its interior angles is 360°. Squares, rectangles, parallelograms, rhombuses, kites and trapeziums are quadrilaterals.

Pentagon

A pentagon has 5 sides and 5 vertices. A regular pentagon has five equal sides and five equal interior angles.

Hexagon

A hexagon has 6 sides and 6 vertices. A regular hexagon can be divided into six equilateral triangles.

Heptagon, octagon, nonagon and decagon

A heptagon has 7 sides, an octagon has 8 sides, a nonagon has 9 sides and a decagon has 10 sides.

Regular and irregular polygons

A regular polygon has all sides equal and all interior angles equal. A square is a regular quadrilateral. An irregular polygon has at least one side or angle that differs from the others.

Circles

A circle is a closed curved shape. Every point on its boundary is the same distance from its centre. The radius runs from the centre to the circle, while the diameter passes through the centre and joins two points on the circle. The diameter is twice the radius.

Types of angles

Acute angle

An acute angle is greater than 0° and less than 90°. The sharp corners in many triangles are acute angles.

Right angle

A right angle measures exactly 90°. The corner of a book or rectangular table is usually a right angle.

Obtuse angle

An obtuse angle is greater than 90° but less than 180°.

Straight and reflex angles

A straight angle measures 180°. A reflex angle is greater than 180° but less than 360°. A complete turn measures 360°.

What are three-dimensional shapes?

A three-dimensional, or 3D, shape has length, width and height. It occupies space and has volume. A cube, cuboid, cylinder, cone and sphere are common 3D shapes.

Face, edge and vertex

A face is a flat or curved surface of a 3D shape. An edge is where two faces meet. A vertex is a corner where edges meet. Curved solids are sometimes described differently in different school books, so check whether curved surfaces are being counted as faces.

Cube

A cube has 6 equal square faces, 12 edges and 8 vertices. A dice is a familiar cube-shaped object.

Cuboid

A cuboid has 6 rectangular faces, 12 edges and 8 vertices. A brick or cereal box is approximately cuboid-shaped.

Cylinder

A cylinder has two equal circular bases joined by a curved surface. A can is a common example.

Cone

A cone has one circular base and a curved surface that narrows to one vertex. An ice-cream cone is a familiar example.

Sphere

A sphere is perfectly round in three dimensions. Every point on its surface is the same distance from its centre. A ball is approximately spherical.

Perimeter, area and volume

Perimeter is the distance around a 2D shape and is measured in units such as centimetres. Area is the space inside a flat shape and is measured in square units such as cm². Volume is the space inside a 3D object and is measured in cubic units such as cm³.

Worked examples

Example 1: Name a six-sided polygon

A polygon with six sides is a hexagon.

Example 2: Find the perimeter of a rectangle

A rectangle is 8 cm long and 3 cm wide. Its perimeter is 2 × (8 + 3) = 22 cm.

Example 3: Classify an angle of 125°

125° is greater than 90° and less than 180°, so it is an obtuse angle.

Common mistakes

A circle has no straight sides and is not a polygon. A side is not the same as a vertex. Perimeter uses ordinary length units, area uses square units and volume uses cubic units. A square is also a rectangle because it has four right angles.

Practice questions

1. How many vertices does a pentagon have? 2. Is a circle a polygon? 3. Name an angle measuring 90°. 4. How many faces does a cube have? 5. Find the perimeter of a square with side 7 cm.

Answers

1. Five. 2. No. 3. A right angle. 4. Six. 5. 28 cm.

Continue learning

Read more about Triangles, Quadrilaterals, Circles and Cuboids.