# Heron's Formula Class 9

Heron’s formula class 9 is used to determine the area of a triangle when the length of all three sides is given. This formula does not involve the use of the angles of a triangle. Heron’s Formula class 9 is a fundamental math concept applied in many fields to calculate various dimensions of a triangle. Therefore, it is crucial for students to understand this formula along with its various applications.

## List of Heron's Formula Class 9

Heron’s Formula class 9 is used to find the area of triangles and quadrilaterals. The formula is used in various ways as shown below.

- Area of a triangle using Heron’s Formula = A = √{s(s - a)(s - b)(s - c)}, where a, b and c are the length of the three sides of a triangle and s is the semi-perimeter of the triangle which is calculated with the formula, s = (a + b + c)/2.
- The area of a quadrilateral whose sides and one diagonal are given can be calculated by dividing the quadrilateral into two triangles using Heron’s formula.
- Area of quadrilateral ABCD = √(s(s - a)(s - d)(s - e)) + √(s'(s' - b)(s' - c)(s' - e)) , Where a, d and e represent the sides of one triangle and b, c and e represent the sides of the other triangle. It should be noted that ‘e’ is the length of the diagonal which is a common side for both triangles.

## Applications of Heron’s Formula Class 9

Heron’s formula is used in various calculations. A few of them are given below.

- Heron’s Formula Class 9 is applied in finding the surface area of triangular plots or agricultural lands. Since not every plot is rectangular in shape, therefore, Heron's formula is of great use in such situations to estimate the cost of such plots.
- Heron’s Formula can be used to determine the area of any irregular quadrilateral by dividing the quadrilateral into triangles. Hence, it can be used to determine the area of irregular plots, parks, farms, etc.

## Tips to Memorize Heron’s Formulas class 9

Students should follow some creative ways to memorize Heron’s formula class 9 and the concepts related to it. It will enable them to use their knowledge of this formula in various situations. It is highly beneficial in real life and for competitive exams.

- Applying and solving problems based on Heron’s Formula to calculate the area of triangles and quadrilaterals is a smart way to memorize the formula and its steps.

- Heron’s Formula is applied in various cases to determine the area of any irregular quadrilateral. Hence students should gain a proper understanding of the basic terms related to triangles and quadrilaterals used in these formulas.

- Students should practice multiple problems and examples given in the textbook. It will provide optimal coverage of the usage of formulas in different contexts.

## Heron’s FormulaClass 9 Examples

**Example 1: **Find the area of a triangle with the side lengths given as 4 units, 6 units, and 8 units respectively.

**Solution:** As we know, a = 4 units, b = 6 units and c = 8 units

Thus, Semi-perimeter, s = (a + b + c)/2 = (4 + 6 + 8)/2 = 9 units

Area of triangle = √[s(s - a)(s - b)(s - c)] = √[9(9 - 4)(9 - 6)(9 - 8)]

⇒ Area of triangle = √(9 × 5 × 3 × 1) = √135 = 11.61 unit^{2}

∴ The area of the triangle is 11.61 unit^{2}

**Example 2:** If the sides of a triangular field are 50 m, 52 m and 34 m find the area of the triangular field.

**Solution** Given, sides of the triangular field are 50 m, 52 m and 34 m

By Heron's formula:

Area of triangle =√(s(s - a)(s - b)(s - c)); where, a, b, c are sides of triangle and semi perimeter (s) = (a + b + c)/2

S = {50 + 52 + 34} / 2 = {136} / 2= 68 m

Area of triangular field = √{68(68 - 50)(68 - 52)(68 - 34) = √68 × 18 × 16 × 34

= √665856

= 816 m^{2}

Students can download the printable **Maths Formulas Class 9** sheet from below.

## FAQs On Heron’s Formula Class 9

### What is the importance of Heron’s Formula?

Heron’s formula is used to obtain the area of a triangle when the length of its three sides is given. It states that the area of a triangle of sides a, b, c is √s(s - a)(s - b)(s - c) where ‘s’ is the semi perimeter = (a + b + c) /2 .

It can also be used as an inefficient way of checking whether a triangle with three given sides can be actually drawn. If the area obtained by Heron’s formula is zero or imaginary (that is, if (s - a)(s - b)(s - c) ≤ 0), then a triangle with sides a, b, c cannot be physically illustrated.

### What are the Basic Heron’s Formulas?

There are different formulas to find the area of various types of triangles. Here is a list of some basic formulas that are used to find the area of a triangle and the area of a quadrilateral using Heron’s formula:

- Heron’s Formula for Area of scalene triangle = √{s(s - a)(s - b)(s - c); where a, b, and c are the 3 sides of a triangle.
- Area of equilateral triangle = (√3 × a
^{2}) / 4; where ‘a’ is the side of the triangle. - Area of Isosceles Triangle = (b/4)√(4a
^{2}- b^{2}); where a is the different side and ‘b’ is the length of the two equal sides of the triangle. - Area of quadrilateral ABCD = √(s(s - a)(s - d)(s - e)) + √(s'(s' - b)(s' - c)(s' - e)), where a, d and e represent the sides of one triangle and b, c and e represent the sides of the other triangle. It should be noted that ‘e’ is the length of the diagonal which is a common side for both triangles.

### How to Memorize Class 9 Heron’s Formula?

Learning class 9 Heron’s formula requires practice and perseverance. With the practice of a wide range of questions based on this formula, students will gain deep knowledge of the core concepts. They will also learn some creative ways to memorize formulas and important theorems. It will enable them to employ their knowledge of formulas in various situations, which is highly useful for facing competitive exams.

### What are the practical applications of Heron’s formula?

There are many practical applications of Heron’s formula. For example, the area of any irregular quadrilateral can be easily calculated by splitting the quadrilateral into triangles. Using Heron's formula, the area of these triangles can be calculated and added together to find the area of the irregular quadrilateral. By using Heron’s formula we can determine the area of irregular plots, parks, farms, etc. Heron's formula is of great use in such situations to estimate the cost of plots.

### Why should students practice questions based on Heron’s formula?

Practicing problems based on Heron’s formula will benefit students to form a deep understanding of each and every term used in this topic. It will also help students to attain problem solving skills required for higher-level studies and competitive exams.

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