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CBSE Area of Parallelograms and Triangles Class 9th Formula

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• Two figures are said to be on same base and between the same parallels, if they have a common side (base) and the vertices (or the vertex) opposite to the common base of each figure lie on a line parallel to the base.

•  Figures on the same base and between the same parallels :

In fig.(i) triangles ABC and DBC have a common side, BC. So we can say that Δ’s ABC and DBC are on the same base BC. Similarly, in figs.(ii), (iii), (iv) this condition can be checked.

Area Axioms: The concept of area possesses properties similar to the concept of the length of a line segment. So, it is natural to think that there may be some analogy between the two concepts:

(a) The concept of length

(b) The concept of area.

Area of a figure is a number associated with the part of the plane enclosed by the figure .

• Two congruent figures have equal area but the converse need not to be true.

• A diagonal of a || gm  divides it into two triangles of equal area.

ar (ΔABD) = ar (ΔCDB) 

• The area of a || gm is the product  of  its  base  and corresponding altitude,

ar (|| gm  ABCD)

= Base × Altitude

• Parallelograms on the same base and between the same parallels are equal in area.

• Triangles on the same base and between the same parallels are equal in area.

• The area of a triangle is half the product of any of its sides and the corresponding altitude.

• In given fig., ar(△ABC) = ½  (BC × AL)

• The area of a trapezium is half the product of its height and the sum of parallel sides.

• The area of a rhombus is half the product of the length of its diagonals.

• Triangles having equal areas and having one side of the triangle, equal to one side of the other, have their corresponding altitudes equal.

Note:

 Diagonals of a parallelogram divide it into four triangles of equal area.

• If the diagonals AC and BD of quad. ABCD intersect at O and separate the quad. Into four triangles of equal area, then the quad. ABCD is a parallelogram.

• A median of a triangle divides it into two triangles of equal area.

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