These comprehensive RBSE Class 9 Maths Notes Chapter 12 Heron’s Formula will give a brief overview of all the concepts.

## RBSE Class 9 Maths Chapter 12 Notes Heron’s Formula

Area of some plane figures :

We recall formulae for areas of some closed plane figures.

1. Area of Square = a^{2} where a is the side of square.

2. Area of Rectangle = l x b where l = length of rectangle, b = breadth of rectangle.

3. Area of Parallelogram = base x height

The height of a ||gm is the distance between its base and the side parallel to the base.

4. Area of rhombus ABCD = base x height

Or

Area of rhombus = \(\frac{1}{2}\) x product of diagonals

= \(\frac{1}{2}\) x AC x BD

Where AC and BD are diagonals.

5. Area of trapezium ABCD …

= \(\frac{1}{2}\) (AB+DC) x h

= (sum of parallel sides) x height

The height of a trapezium is the distance between its parallel sides.

6. Area of a triangle with given base and height is written as :

Area of ΔABC = \(\frac{1}{2}\) x base x height

7. Area of a right triangle = \(\frac{1}{2}\) x base x perpendicular

8. Area of an equilateral triangle = \(\frac{\sqrt{3}}{4}\) (side)^{2}.

9. Area of an isosceles triangle = \(\frac{a \sqrt{4 b^{2}-a^{2}}}{4}\) units.

Where, b is the length of equal sides and a is the length of third side.

10. Perimeter and semi-perimeter of a triangle \(s=\frac{a+b+c}{2}\)

Where, denotes the semi-perimeter of ΔABC.

11. Area of a Triangle – by Heron’s Formula.

The famous formula given by Heron about the area of a triangle in terms of its three sides is also known as Heron’s formula.

Consider a triangle ABC in which BC = ‘a’ units CA = ‘b’ units and AB – ‘c’ units (see figure).

Let S = semiperimeter, i.e. half the perimeter of the triangle.

Heron’s formula is stated as

Area of triangle \(A B C=\sqrt{s(s-a)(s-b)(s-c)}\) sq. units

12. Area of a quadrilateral whose side and one diagonal are given, can be calculated by dividing the quadrilateral into two triangles and using the Heron’s formula.

CBSE provides Class 10 Maths Formulas Chapter wise in the PDF format as per latest NCERT Syllabus.

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