# NCERT Class 9 MathematicsHerons Formula (Mensuration) Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Mensuration**

It is branch of mathematics which is concerned about the measurement of length, area and Volume of plane and Solid figure

**Perimeter**

The perimeter of plane figure is defined as the length of the boundary

It units is same as that of length i.e.. m, cm, km

1 Meter | 10 Decimeter | 100 centimeter |

1 Decimeter | 10 centimeter | 100 millimeter |

1 Km | 10 Hectometer | 100 Decameter |

1 Decameter | 10 meter | 1000 centimeter |

Area

The area of the plane figure is the surface enclosed by its boundary

It unit is square of length unit. i.e..

1 square Meter | 100 square Decimeter | 10000 square centimeter |

1 square Decimeter | 100 square centimeter | 10000 square millimeter |

1 Hectare | 100 square Decameter | 10000 square meter |

1 square myraimeter | 100 square kilometer | square meter |

**Perimeter and Area of different figure**

N | Shape | Perimeter/height | Area |

1 | Right angle triangle Base = b, Height = h Hypotenuse = d | P Height = h | |

2 | Isosceles right angled triangle Equal side = a | Height = a | |

3 | Any triangle of sides a , b, c | Where This is called Heron՚s formula (sometimes called Hero՚s formula) is named after Hero of Alexandria | |

4 | Square Side = a | ||

5 | Rectangle of Length and breath L and B respectively | ||

6 | Parallelograms Two sides are given as a and b | When the diagonal is also given, say d Then Where | |

7 | Rhombus Diagonal and are given | ||

8 | Quadrilateral (a) All the sides are (b) Both the diagonal are perpendicular to each other (c) When a diagonal and perpendicular to diagonal are given | (a) P | (a) Where (b) where and are the diagonal (c) where d is diagonal and and are perpendicular to that |