NCERT Class 9 Maths Formula CBSE Board Sample Problems Part 9

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9. Area of Parallelogram

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.

Area of figure

Area of Figure

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2

Properties of Area

1) Two congruent figures have same area

Two congruent

Two Congruent

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Two congruent

Two Congruent

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

If two figure have same area, they are not necessary congrue …

If Two Figure Have Same Area

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If two figure have same area, they are not necessary congrue …

If Two Figure Have Same Area Not Necessary Congruent

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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

Properties of Area

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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.

Figure on the same base and between same parallels

Figure on the Same Base and between Same Parallels

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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 Area of parallelogram

Area of Area of Parallelogram

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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 parallelogram ABCD

Area of Parallelogram ABCD

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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

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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