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.

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