## Solid Shapes

Solid shapes are three dimensional shapes who have length, breadth and height as the three dimensions.

Here are a few solid shapes.

### Solid shapes have faces, edges and vertices.

## Polyhedron

A solid shape whose faces are all polygons is called a **polyhedron**.

### Pyramid

A pyramid is a polyhedron with: a polygon as its base and all other faces as triangles that meet at a point (Apex).

**Given below is a table showing the number of faces, edges, vertices for different polyhedrons.**

Solid Shapes |
Faces |
Edges |
Vertices |

Triangular pyramid (It's also called a Tetrahedron.) |
4 | 6 | 4 |

Square Pyramid |
5 | 8 | 5 |

Pentagonal Pyramid |
6 | 10 | 6 |

### Prism

A prism is a polyhedron with two identical faces that are parallel and all other faces as parallelograms.

**Given below is a table showing the number of faces, edges, vertices for different types of prisms.**

Solid Shapes |
Faces |
Edges |
Vertices |

Triangular Prism |
5 | 9 | 6 |

Square Prism |
6 | 12 | 8 |

Pentagonal Prism |
7 | 15 | 10 |

### Formula - Euler’s formula

For every polyhedron, the value of \(F + V – E\) is . This formula is called **Euler’s formula**.

Let’s consider a few examples,

Shape |
Faces |
Edges |
Vertices |
\(F + V – E\) |

5 | 8 | 5 | 5 + 5 - 8 = 2 | |

6 | 12 | 8 | 6 + 8 - 12 = 2 |

## Tips and tricks

**Tip:**Make these shapes using plain sheet of paper. This would help visualise the solid shapes.**Tip:**Using the geosolid, move your finger along each shape to understand the concept of faces, edges and vertices.**Tip:**Use a paper that has grid lines on it. The grid lines make it easy to see if the line of symmetry is dividing the figure into two identical parts.**Tip:**Draw a free hand design on an A4 sheet. Now fold the paper in to one half. If the figure is exactly symmetrical than one part should match the other.

### Common mistakes or misconceptions

**Misconception 1:** A line of symmetry is always vertical.

A line of symmetry can be vertical, horizontal or diagonal as long as it divides the figure into two identical parts.

## Test your knowledge

1. Which is a pentagonal pyramid?

2. Which is a pentagonal prism?

3. Which is a hexagonal prism?

4. Draw all the possible lines of symmetry for each letter of the English alphabet. Also write in the number of lines of symmetry.

a. Number of lines of symmetry ________________________

b. Number of lines of symmetry________________________

c. Number of lines of symmetry________________________

5. Write yes or no if the first figure is the mirror image of the second figure, about the given line \(l.\)

a.

b.