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Facts that Matter- Areas of Parallelograms and Triangles - Class 9 PDF Download

Areas of Plane Figures

Facts that Matter- Areas of Parallelograms and Triangles - Class 9

  • Two congruent figures have equal areas.
  • A diagonal of a parallelogram divides it into two triangles of equal area.
  • Parallelograms on the same base (or equal base) and between the same parallels are equal in area.
  • Triangles on the same base (or equal bases) and between the same parallels are equal in area.
  • Area of a parallelogram = base x height.
  • Area of a triangle Facts that Matter- Areas of Parallelograms and Triangles - Class 9
  • A median of a triangle divides it into two triangles of equal area.
  • Diagonals of a parallelogram divides it into four triangles of equal area.

Remember:

  • The part of the plane enclosed by a simple closed figure is called a planar region.
  • The measure of a planar region is called its area.
  • Two figures are called congruent, if they have the same shape and the same size.
  • If two plane figures are congruent, they have equal areas.
  • Two plane figures having equal areas need not to be congruent.

Figures on the same Base and between the same Parallels

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

Note: 
Out of the two parallels one must be the line containing the common base.

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FAQs on Facts that Matter- Areas of Parallelograms and Triangles - Class 9

1. What are the formulas to calculate the area of a parallelogram and a triangle?
Ans. The formula to calculate the area of a parallelogram is base multiplied by the height. For a triangle, the formula is half of the base multiplied by the height.
2. How can I determine the base and height of a parallelogram or a triangle?
Ans. The base of a parallelogram is any one of its sides, and the height is the perpendicular distance between the base and the opposite side. In a triangle, the base is any one of its sides, and the height is the perpendicular distance from the base to the opposite vertex.
3. Can the area of a parallelogram or a triangle be negative?
Ans. No, the area of a parallelogram or a triangle cannot be negative. Area is a measure of the amount of space occupied by a figure, and it is always a positive value or zero.
4. What is the significance of figures having the same base and being between the same parallels?
Ans. When two figures have the same base and are between the same parallels, their areas are equal. This property is useful in solving problems involving comparing or calculating the areas of different figures.
5. Can you provide an example of how to calculate the area of a parallelogram or a triangle using the given formulas?
Ans. Sure! Let's say we have a parallelogram with a base of 6 cm and a height of 4 cm. The area of the parallelogram would be 6 cm (base) multiplied by 4 cm (height), which equals 24 square cm. Similarly, for a triangle with a base of 5 cm and a height of 8 cm, the area would be half of 5 cm (base) multiplied by 8 cm (height), which equals 20 square cm.
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