Solid figures
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In this lesson, you will learn
- What solid figures and polyhedra are
- How to recognize prisms, pyramids, cones, cylinders and spheres
- Real-life examples of solid figures
- The five Platonic solids
What Are Solid Figures?
Solid figures, also called solid shapes, are three-dimensional figures that have length, width and height.
A polyhedron is a three-dimensional figure whose surfaces are polygons.
See some examples of three-dimensional figures below.
A face is a flat surface of a solid, an edge is where two faces meet, and a vertex is a corner where edges meet.
Is a circle a solid figure?
Show answer
No. A circle is flat. It has only length and width, so it has 2 dimensions, not 3.
Prisms: Rectangular Prism, Triangular Prism and Cube
A prism is a polyhedron with two faces that are congruent and parallel. These faces are called bases.
Other faces of the prism are called lateral faces, and they are parallelograms. Some examples of prisms are rectangular prisms, triangular prisms, pentagonal prisms, hexagonal prisms, and so on.
Rectangular prism
A rectangular prism is shown above. Notice that the rectangular prism is made of two parallel faces that are polygons. These parallel faces are rectangles in this case and they are congruent. Looking at the figure, the bases are the top and bottom faces. The other four faces are called lateral faces.
Triangular prism
A triangular prism is shown below. It is a prism with two triangular faces that are congruent. The other three faces are rectangles and they are called lateral faces.
Cube
A cube is also a prism with congruent squares as bases (or sides) and lateral faces. The difference between a cube and a rectangular prism is that you can pick any two opposite faces as your bases, since all the faces are congruent. The following figure is a cube.
- All its faces are polygons, so it is a polyhedron.
- It has two faces that are congruent and parallel, so it is a prism. The two triangles are the bases.
- A prism is named after its bases. The bases are triangles.
It is a triangular prism.
Thinking the bases are always the top and bottom. The bases are the two congruent, parallel faces, wherever they are. A triangular prism lying on its side still has its two triangles as bases.
Which faces are the bases of a triangular prism?
Show answer
The two triangles. They are congruent and parallel. The three rectangles are the lateral faces.
Pyramids
A pyramid is a polyhedron in which one face, also called the base, can be any polygon. The other faces, also called lateral faces or triangular sides, are triangles that meet at a common vertex. The following figure is a square pyramid. However, a pyramid could be a pentagonal pyramid if the base is a pentagon or a hexagonal pyramid if the base is a hexagon.
Prisms and pyramids are named after the shape of their base. A pyramid has one triangle for each side of its base.
What do you call a pyramid whose base is an octagon?
Show answer
An octagonal pyramid. It has 8 triangular faces, one for each side of the octagon.
Cones, Cylinders and Spheres
Cone
A cone has a circular base connected to a vertex. Suppose the base of a pyramid is a regular polygon. You can turn the pyramid into a cone by continuously increasing the number of sides of the base of the pyramid. The following figure is a cone.
Cylinder
A cylinder has two congruent or equal circular bases that are parallel. The following figure is a cylinder.
Sphere
A sphere is a figure with a curved surface in which all points on the surface are the same distance from the center. Because a sphere is round, it could be a little hard to accept that it has 3 dimensions. Here is how to look at it. If a sphere did not have 3 dimensions, then it would be flat just like a circle. The following figure is a sphere.
Cones, cylinders and spheres have curved surfaces, so they are solid figures but not polyhedra.
Why is a cylinder not a polyhedron?
Show answer
Because not all of its surfaces are polygons. Its bases are circles and its side is curved.
Real-Life Examples of Solid Figures
- Earth, marbles and soccer balls are examples of spheres.
- Soda cans, candles, and paint cans are examples of cylinders.
- Ice cream cones, traffic cones, and carrots are examples of cones.
- The Rubik's cube and ice cubes are examples of cubes.
- The Egyptian pyramids are examples of pyramids.
- A stick of butter, a laptop, refrigerators, and cereal boxes are examples of rectangular prisms.
A basketball is an example of which solid figure?
Show answer
A sphere. It is round, and every point on its surface is the same distance from its center.
Platonic Solids: Other Interesting Solid Figures
These solid figures are specifically called Platonic solids or regular polyhedra. Just like a regular polygon whose sides are all equal, all faces of a regular polyhedron are equal regular polygons, and the same number of faces meet at every vertex. There are five Platonic solids!
- Tetrahedron
- Cube
- Octahedron
- Icosahedron
- Dodecahedron
Tetrahedron
A tetrahedron, also called triangular pyramid, is a Platonic figure that has four faces. All four faces are equilateral triangles. Notice that the tetrahedron has a triangular base. The following figure is a tetrahedron.
Cube
A cube is a Platonic figure that has six equal faces. All six faces of a cube are squares. The following figure is a cube.
Octahedron
An octahedron is a Platonic figure that has eight equal faces. All eight faces of an octahedron are equilateral triangles and the octahedron is called a regular octahedron. Notice that to create an octahedron, you just need to join the square bases of two square pyramids whose triangular faces are equilateral. The following figure is an octahedron.
Icosahedron
An icosahedron is a Platonic figure that has twenty faces. All twenty faces of an icosahedron are equilateral triangles. The following figure is an icosahedron.
Dodecahedron
A dodecahedron is a Platonic figure that has twelve faces. All twelve faces of a dodecahedron are regular pentagons. The following figure is a dodecahedron.
Which Platonic solid is also a prism?
Show answer
The cube. Any two opposite squares are congruent and parallel, so they can be the bases.
Summary
- Solid figures have three dimensions: length, width and height.
- A polyhedron is a solid whose surfaces are all polygons.
- A prism has two congruent, parallel bases; a pyramid has one base and triangles that meet at a vertex. Both are named after their base.
- Cones, cylinders and spheres have curved surfaces, so they are not polyhedra.
- There are five Platonic solids: the tetrahedron (4 faces), cube (6), octahedron (8), dodecahedron (12) and icosahedron (20).
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