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

Area of Parallelogram
S. noTermsDescriptions
1Area of figureArea of a figure is a number (in some unit) associated with the part of the plane enclosed by that figure.
Area of Figure
2Properties of Area(1) Two congruent figures have same area
Two Congruent
Two Congruent

(2) If two figures have same area, they are not necessary congruent

If Two Figure Have Same Area
If Two Figure Have Same Area 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.

Properties of Area
3Figure on the same base and between same parallelsTwo 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.
Figure on the Same Base and between Same Parallels

In the above figure triangle and parallelogram are on the same base and between same parallel

4Parallelogram on same base and between same parallelParallelograms on the same base (or equal bases) and between the same parallels are equal in area.

Area of Parallelogram ABCD = Area of Parallelogram PBCQ

5Area of Area of parallelogramArea of Area of parallelogram is equal base multiplied by

Parallelogram Height

Area of Area of Parallelogram

Area of Parallelogram = Height X Base

Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallel

6Triangles 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 Parallelogram ABCD

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

Area of triangle ABD = Area of triangle ACB

7Area 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

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