Geometric shapes can be 2 dimensional or 3 dimensional.

Two dimensional figures are the figures which are drawn on a 2D plane. Examples for 2 dimensional figures are

- circle
- triangle
- rectangle
- square
- pentagon
- hexagon
- septa
- octagon etc.

Three dimensional shapes are the shapes which have 3 dimensions like length, width and height. the real life examples a re foot ball, basket ball, bricks etc.

Examples for 3dimensional shapes are:

- sphere
- cube
- cuboid
- prism
- pyramid etc.

Since, the 2D figure have only 2 dimensions, **the units for area is unit ^{ 2 }**,and the 3D shapes have 3 dimensions ,

**the units for volume is unit**

^{3}**Proportions for 2d figures**

before we go for conversion of area of 2D figures, we need to know how the units of length are related.

10 ^{-3} m | mm | Millimeter |

10 ^{-2} m | cm | centimeter |

10 ^{-1} m | dm | decimeter |

10 ^{1} m | dam | decimeter |

10 ^{2} m | hm | hectometer |

10 ^{3 }m | km | kilometer |

- When we need to convert the units in to another units then we need identify the conversion factor.
- Multiply the square of the conversion factor with the arae of 2D figure.
- We will get the area in required units.

**conversion units**

km | hm | dam | dm | cm | mm | |

km | 1 | 10 | 100 | 10000 | 100000 | 1000000 |

hm | 0.1 | 1 | 10 | 1000 | 10000 | 100000 |

dam | 0.01 | 0.1 | 1 | 100 | 1000 | 10000 |

dm | 0.0001 | 0.001 | 0.01 | 1 | 10 | 100 |

cm | 0.00001 | 0.0001 | 0.001 | 0.1 | 1 | 10 |

mm | 0.000001 | 0.00001 | 0.0001 | 0.01 | 0.1 |

**Example:**

Area of a rectangle is 30 cm ^{2}, convert it in to decimeters.

**solution:**

From the table, conversion factor is 1 cm=0.1dm

so, area in dm= 30 x (0.1 dm) ^{2 }

=30 x 0.01 dm ^{2}

=0.3 dm ^{2}

**Example 2:**

Area of a rectangle is 300 cm ^{2}, convert it in to meters.

**Solution:**

From the table, conversion factor is 1 cm=0.01m

so, area in dm= 300 x (0.01 m) ^{2 }

=300 x 0.0001 m ^{2}

=.003 m ^{2}