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

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## 9. Area of Parallelogram

S. no | Terms | Descriptions |

1 | Area of figure | Area of a figure is a number (in some unit) associated with the part of the plane enclosed by that figure. |

2 | Properties of Area | (1) Two congruent figures have same area (2) If two figures have same area, they are not necessary congruent (3) If a planar region formed by a figure T is made up of two non-overlapping planar regions Formed by figures P and Q, then ar (T) = ar (P) + ar (Q) , where ar (X) denotes the area of Figure X. |

3 | Figure on the same base and between same parallels | Two figures are said to be on the same base and between the same parallels, if they have a common base (side) and the vertices, (or the vertex) opposite to the common base of each figure lies on a line parallel to the base. In the above figure triangle and parallelogram are on the same base and between same parallel |

4 | Parallelogram on same base and between same parallel | Parallelograms on the same base (or equal bases) and between the same parallels are equal in area. Area of Parallelogram ABCD = Area of Parallelogram PBCQ |

5 | Area of Area of parallelogram | Area of Area of parallelogram is equal base multiplied by Parallelogram Height Area of Parallelogram = Height X Base Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallel |

6 | Triangles and Parallelogram | (a) If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of parallelogram Area of triangle ABD = Area of triangle ACB Area of triangle ADB (b) Triangles on the same base (or equal bases) and between the same parallels are equal in area Area of triangle ABD = Area of triangle ACB |

7 | Area of Triangle | (1) Area of triangle is given by (2) Triangles on the same base (or equal bases) and having equal areas lie between the same parallels |