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Summary

  • Area of a figure is a unit associated with the part of the plane enclosed by that figure.
  • Two congruent figures have equal areas but the figures having equal areas need not be congruent.
  • If a planar region formed by a figure X is made up of two non-overlapping planar regions formed by figures A and B, then ar (X) = ar (A) + ar (B), where ar (P) denotes the area of figure P.
  • Two figures are said to be on the same base and between the same parallels, if they have a common base and the vertices opposite to the common base of each figure lie on a line parallel to the base.
  • Parallelograms on the same base and between the same parallels are equal in area.
  • Area of a parallelogram is the product of its base and the corresponding altitude.
  • Parallelograms on the same base and having equal areas lie between the same parallels.
  • 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 the parallelogram.
  • Triangles on the same base and between the same parallels are equal in area.
  • Area of a triangle is half the product of its base and the corresponding altitude.
  • Triangles on the same base and having equal areas lie between the same parallels.
  • A median of a triangle divides it into two triangles of equal areas.




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