Geometric Shapes – Names, Types, and Properties
Updated on October 14, 2026
Geometric shapes are figures made of points, lines, curves, or surfaces, like triangles, circles, cubes, and spheres. They are the building blocks of geometry and are either two-dimensional (flat, with length and width) or three-dimensional (solid, with length, width, and height).
Geometric shapes definition
Geometric shapes are mathematical figures defined by points, lines, curves, or surfaces. Every shape has properties you can describe and measure, such as the number of sides, angles, faces, edges, and vertices. These properties are what make one shape different from another.
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Types of geometric shapes
Shapes in geometry are classified into two main types according to their dimensions: two-dimensional (2D) shapes and three-dimensional (3D) shapes.
Two-dimensional geometric shapes
Unlike three-dimensional geometric shapes, two-dimensional geometric shapes do not have any depth. There is no volume to them, as they lie entirely on a plane. The boundaries of these shapes are defined by points, lines, and curves.
2D shapes have the following key features:
- They are flat.
- There are only two dimensions – length and width.
- Perimeters and areas can be measured.
The following are common 2D shapes:
A circle, triangle, square, rectangle, pentagon, hexagon, etc.
Three-dimensional geometric shapes
Three-dimensional geometrical shapes have length, width, and height (depth). It is physically possible to touch and hold these math shapes because they occupy space and have volume.
Key features of 3D shapes:
- They have three dimensions: length, width, and height.
- Have faces, edges, and vertices (depending on the shape).
- Can be measured with surface area and volume.
Common 3D shapes in geometry include: Cube, sphere, cylinder, cone, pyramid, prism, etc.
List of geometric shapes & their properties
Triangle
A triangle is formed by connecting three line segments, so it has 3 sides, 3 angles, and 3 vertices. Its three interior angles always add up to 180°. Triangular objects include pizza slices, nachos, and road warning signs. The name of a triangle depends on its angles and sides. For example, a right triangle has one 90° angle.
An acute triangle has three angles that are all less than 90°. An obtuse triangle has one angle greater than 90°. An equilateral (equiangular) triangle has three equal sides and three equal 60° angles.
Circle
A circle is a round 2D shape with no straight sides and no corners. Every point on a circle is the same distance from its center.
A pizza or a wheel is an example of a circular object. A circle always has a radius — a line from its center to any point on its edge. Radius is essentially half the length of the diameter (the whole line from one edge of the circle to another).
Square
A square is a four-sided shape made of four equal line segments. Like a rectangle, it has four right angles. Square objects include chessboards, sticky notes, and window panes.
The key properties:
- Four equal sides.
- Four 90° (right) angles.
- Opposite sides are parallel.
Rectangle
A rectangle is a four-sided shape with four right angles. Its opposite sides are equal in length and parallel. A square is a special rectangle with all four sides equal, so every square is a rectangle, but not every rectangle is a square.
A laptop screen, a door, and a book cover are all examples of rectangles.
Parallelogram
A parallelogram is a four-sided shape formed by joining four points with four straight lines. In a parallelogram, opposite sides are equal in length and parallel to each other, while opposite angles are also equal. Unlike rectangles or squares, its angles are not necessarily right angles.
Examples of parallelogram-shaped objects include slanted tiles, patterned floor designs, and some book covers viewed at an angle.
Polygons
A polygon is a closed 2D shape made only of straight sides, such as a triangle, square, pentagon, or hexagon. Circles and ovals are geometric shapes too, but they are not polygons because their edges are curved.
Three-dimensional shapes
Cube
A cube is a three-dimensional shape made of six identical square faces. All edges are equal in length, and every angle is a right angle.
Key properties:
- There are 6 square faces.
- There are 12 equal edges.
- A total of 8 vertices (corners) are present.
A die or a Rubik’s Cube is a common example.
Cylinder
A cylinder consists of two circular bases connected by a curved surface. The bases are equal in size and parallel. Cylindrical objects include soda cans and paper towel rolls.
Key properties:
- It has two congruent (identical) and parallel circular bases.
- A curved surface connects the bases.
- The axis of a right cylinder is perpendicular to its base; an oblique cylinder is not.
- When a cylinder is unfolded, its curved surface becomes a rectangle (height × circumference).
Sphere
Unlike shapes with edges or corners, a sphere is perfectly round. Every point on its surface is the same distance from the center. Soap bubbles take on a spherical shape, and the Earth is close to a sphere too.
Balls and oranges are examples of spheres.
Cone
A cone combines one circular base with a single pointed vertex at the top. Its curved surface narrows smoothly toward the vertex.
Cone properties:
- It has one circular base.
- It has one curved surface.
- It has one vertex, called the apex.
An ice-cream cone, a party hat, and a funnel are all cone-shaped.
Open and closed shapes
2D shapes can be either open or closed. A closed shape has a boundary with no gaps, while an open shape has ends that don’t meet.
Closed shapes
Closed geometric shapes don’t have open ends and can be traced back without breaking.
Below are some examples of closed shapes:
- Triangles are closed figures with three sides and three vertices.
- A circle is a closed shape with one curved side and no vertices.
- Having four sides and four vertices, a quadrilateral is a closed shape. Examples of a quadrilateral are a square, a rectangle, a rhombus, a parallelogram, a trapezoid, etc.
- With five sides and five vertices, a pentagon is a closed shape.
- Hexagons are closed shapes that have 6 sides and 6 vertices.
Besides the closed shapes mentioned above, there are many others, including the heptagon, the octagon, the decagon, and the oval. Polygons are closed shapes made up of straight lines.
Open shapes
A shape with a different start point and endpoint is called an open shape. Open shapes are not continuous and cannot be traced without any breaks. The letter C is an example of an open shape.
Weird shape names
Beyond the basic shapes, geometry has some unusual ones you may not have heard of before:
Reuleaux triangle
Reuleaux triangles are curved triangles with rounded sides so that the distance across the shape is constant regardless of direction. It can rotate inside a square while always touching all four sides, which makes it useful in engineering, for example, in drills that cut square holes.
Polyomino
Polyominoes are flat shapes formed by joining one or more equal squares edge to edge. Among the different types are dominoes (2 squares), trominoes (3), tetrominoes (4), and pentominoes (5). These pieces are widely used in puzzles and tiling problems.
Sphericon
A sphericon is a 3D solid with one continuous curved surface and one edge made of two semicircles. When it rolls, it wobbles from side to side, and every point of its surface touches the ground.
Gabriel’s Horn (Torricelli’s Trumpet)
The Gabriel’s horn is a geometric figure whose surface area is infinite, but its volume is finite. It is famous in calculus for a puzzle known as the painter’s paradox.
The painter’s paradox shows this surprising property:
- The inside of the horn can only be filled with a finite amount of paint (since it has a finite volume).
- Despite this, covering its outer surface would take an infinite amount of paint (since its surface area is infinite).
Lentoid
A lentoid is a lens-shaped 3D body. Seen from the front, it looks like a circle, and seen from the side, it looks like a convex lens. The term is used in geometry, as well as in biology and jewelry, to describe lens-like forms.
Real-life applications of geometric shapes
Geometric shapes are not just abstract math concepts — they appear everywhere in everyday life. Architects and engineers use triangles, rectangles, and cylinders to design strong buildings, bridges, and tunnels. Circles and spheres are essential in wheels, balls, gears, and pipes because they allow smooth motion and even distribution of force.
In technology and design, screens, books, and tables are often rectangular, while cubes and prisms are common in packaging and storage. Nature also follows geometric patterns: honeycombs form hexagons for efficiency, planets resemble spheres, and snowflakes show symmetrical polygon shapes. Learning geometric shapes helps children better understand the world around them and see how math connects to real objects and practical problem-solving.
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Solved examples on geometry shapes
Example 1: How many faces does a rectangular prism have?
Solution: A rectangular prism has six faces, twelve edges, and eight vertices.
Example 2: What do you call a triangle with one right angle?
Solution: A triangle with one right angle is called a right-angled triangle.
Example 3: Is a cone an open shape or a closed shape?
Solution: A cone is a closed shape because its base and curved surface enclose space.
Example 4: How many sides does a heptagon have?
Solution: A heptagon has seven sides and seven angles.
Example 5: What type of polygon has all sides and angles equal and has eight sides?
Solution: A polygon with eight equal sides and angles is called a regular octagon.
Practice problems on geometric shapes
- A rectangle has:
- 4 equal sides
- 2 pairs of equal sides
- none of these
- 3 pairs of equal sides
- The line passing through the center of a circle connecting two points of it is called:
- diameter
- radius
- chord
- circumference
- Among all the types of shapes in geometry, a cylinder is a:
- one-dimensional shape
- two-dimensional shape
- three-dimensional shape
- none of these
- A pentagon with all equal sides and angles is called:
- open pentagon
- hexagon
- closed pentagon
- regular pentagon
Answers: 1) b, 2) a, 3) c, 4) d.
Frequently Asked Questions on Geometric Shapes
What are geometric shapes?
Geometric shapes are figures formed by points, lines, curves, or surfaces. They can be two-dimensional, like squares and circles, or three-dimensional, like cubes and spheres, each having defined properties such as sides, angles, and symmetry.
How did geometric shapes get discovered?
Geometric shapes were studied by ancient civilizations such as the Egyptians, Babylonians, and Greeks, who used them in building and land measurement. Around 300 BCE, the Greek mathematician Euclid organized these ideas in his book Elements, laying the groundwork for modern geometry.
What are some geometric shapes?
Common geometric shapes include triangles, squares, rectangles, circles, cubes, spheres, cones, and others. There are also unusual forms like sphericons and Reuleaux triangles.
How many geometric shapes are there?
There is no fixed number of geometric shapes. Basic geometric shapes, 2D and 3D, are well-known, but mathematically, shapes are infinite, including polygons, polyhedra, curved shapes, and complex forms used in higher mathematics and design.
Geometric shapes worksheets
Here you can find free online shape worksheets (basic to advanced) that help with identifying shapes, understanding sides and symmetry, recognizing geometric properties:
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