## Three-Dimensional Figures

Three-dimensional figures are discussed here with the figures or pictures along with the explanation.

**Solids: **Objects having fixed shape and size, and occupying fixed space are called solids.

Solids occur in various geometrical shapes. These shapes are known three-dimensional figures.

Some 3-D shapes are namely cuboids, cubes, cylinders and cones.

We will discuss about some of the 3-dimensional figures having flat faces, namely cubes, cuboids, prisms, pyramids and tetrahedrons.

### Faces, Vertices and Edges of a 3-dimensional Figure:

(i)

**Faces: ** Each flat part of a solid is called its face.

(ii)

**Vertices: ** Each corner where three faces of a solid meet is called its vertex. The plural of vertex is vertices.

(iii)

**Edges: ** The two faces of a solid meet in a line, called an edge.

Now, we shall discuss about the faces, vertices and edges of some 3-dimensional figures having flat faces.

Name of Solid | Number of Faces | Number of Vertices | Number of Edges |
---|

Cuboid | 6 | 8 | 12 |

Cube | 6 | 8 | 12 |

Triangular Prism | 2 triangular, 3 rectangular | 6 | 9 |

Square Pyramid | 1 square face, 4 triangular faces | 5 | 8 |

Rectangular Pyramid | 1 rectangular face, 4 triangular faces | 5 | 8 |

Triangular Pyramid (or Tetrahedron) | 4 triangular faces | 4 | 6 |

### I. Cuboid:

*A solid bounded by six rectangular plane faces is called a ***cuboid**.A box, a matchbox, a book, a brick, a tile, etc., are all in the shape of a cuboid.

In the adjoining figure, ABCDEFGH is a cuboid.

(i) **Faces of a Cuboid: **

*A cuboid has 6 faces. *

In the given figure, the 6 faces of the cuboid are:

*ABCD, EFGH, ADHE, BCGF, ABFE and DCGH. *

(ii) **Vertices of a Cuboid: **

*A cuboid has 8 vertices.*

In the given figure, the 8 vertices of the cuboid are:

*A, B, C, D, E, F, G, H. *

(iii) **Edges of a Cuboid: **

*A cuboid has 12 edges. *

In the given figure, the 12 edges of the cuboid are:

* AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG. *

### II. Cube:

*A cuboid whose length, breadth and height are equal is called a ***cube. **Dice, sugar cubes, ice cubes, etc., are all examples of a cube.

In the adjoining figure, ABCDEFGH is a cube.

(i) **Faces of a Cube: **

* A cube has 6 faces. *

In the given figure, the 6 faces of the cube are:

*ABCD, EFGH, ADHE, BCGF, ABFE and DCGH.*

(ii) **Vertices of a Cube: **

*A cube has 8 vertices. *

In the given figure, the 8 vertices of the cube are:

*A, B, C, D, E, F, G, H. *

(iii) **Edges of a Cube: **

*A cube has 12 edges. *

In the given figure, the 12 edges of the cube are:

*AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG. *

**Note: **

Here, in three-dimensional figures we will discuss about right prism arid regular pyramid.

### III. PRISM:

* A solid whose two faces are parallel plane polygons and the side faces are rectangles is called a ***prism. ** **Triangular Prism: ** *A ***triangular prism** is made up of two parallel end-faces each one of which is a triangle and three lateral faces each one of which is a rectangle. In the adjoining figure,

*ABCDEF* is a triangular prism.

(i) **Faces of a Triangular Prism: **

*A triangular prism has 2 triangular faces and 3 rectangular faces. *

In the given figure,

2 triangular faces are ∆ABC and ∆DEF,

3 rectangular faces are ABED, ADFC and CBEF.

(ii) **Vertices of a Triangular Prism: **

*A triangular prism has 6 vertices. *

In the given figure, the 6 vertices of the triangular prism are A, B, C, D, E, F.

(iii) **Edges of a Triangular Prism: **

*A triangular prism has 9 edges. *

In the given figure, the 9 edges of the triangular prism are:

AB, BC, CA, DE, EF, FD, AD, BE, CF

**Note: **

A cuboid is also called a rectangular prism.

### IV. PYRAMID:

*A pyramid is a solid whose base is a plane rectilinear figure whose side faces are triangles having a common vertex, called the vertex of the ***pyramid.**** (a) Square Pyramid: **It is a solid whose base is a square and whose side faces are triangles having a common vertex.

In the adjoining figure, OABCD is a square pyramid with its vertex at O.

(i) **Vertices of a Square Pyramid: **

*A square pyramid has 5 vertices. *

In the given figure, OABCD is a square pyramid having O, A, B, C, D as its vertices.

(ii) **Faces of a Square Pyramid: **

*A square pyramid has faces one of which is a square face and the rest four are triangular faces.*

In the given figure, OABCD is a square pyramid having ABCD as its square face and OAD, OCD, OBC and OAB as its triangular faces.

(iii) **Edges of a Square Pyramid: **

*A square pyramid has 8 edges. *

In the given figure, the square pyramid OABCD has 8 edges, namely, AB, BC, CD, DA, OA, OB, OC and OD.

**(b) Rectangular Pyramid:**

*It is a solid whose base is a rectangle and whose side faces are triangles having a common vertex. *

In the adjoining figure, OABCD is a rectangular pyramid.

(i) It has 5 vertices, namely O, A, B, C, D.

(ii) It has 1 rectangular face, namely ABCD, and 4 triangular faces, namely OAD, ODC, OAB, OBC

(iii) It has 8 edges, namely AB, BC, CD, DA, OA, OB, DC, OD

** (c) Triangular Pyramid (Tetrahedron): **

* It is a solid whose base is a triangle and whose side faces are triangles having a common vertex. *

In the adjoining figure, OABC is a triangular pyramid.

(i) It has 4 vertices, namely O, A, B, C.

(ii) It has 4 triangular faces, namely ABC, OAB, OAC and OBC.

(iii) It has 6 edges, namely OA, OB, OC, AB, AC, BC.

**Related Links:**

**Three-Dimensional Figures**

**Three-Dimensional Figures**

**Three-Dimensional Figures - Worksheets****Worksheet on Three Dimensional Figures**

8th Grade Math Practice

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