Heron’s Formula Class 9

What is Heron’s Formula?

Heron’s formula helps determine the area of a triangle if the value of the length of all the sides of the triangle is given. Heron’s formula is also used for finding the area of a quadrilateral as a quadrilateral can easily be divided into two triangles by the diagonals of the quadrilateral. According to this formula, the area of a triangle is directly proportional to the square root of the semi-perimeter of the triangle. If the sides of the triangle are a, b, and c then Heron’s Formula is,...

Heron’s Formula Definition

Heron’s formula, states that “For a triangle having lengths, a, b, and c, and semi-perimeter of the triangle is ‘s’ the area of the triangle using Heron’s Formula” is discussed in the image above....

History of Heron’s Formula

In 60 CE Heron of Alexandria gave a formula which is known as the Heron’s Formula. Heron was a Greek Mathematician who gave the formula for finding the area of a triangle when the length of all sides of the triangle is given. He used this formula for solving various problems in triangles and trigonometry. He proved the Law of Cosine and the Law of Cotangent using this formula....

Proof of Heron’s Formula

Heron’s formula is derived using Pythagoras Theorem, the Area of a Triangle, and others. For a triangle having lengths of sides, a, b, and c. The semi-perimeter of the triangle ABC is “s”,...

Heron’s Formula Derivation Using Pythagoras Theorem

The proof for Heron’s Formula is discussed in the article below...

Heron’s Formula Derivation Using Cosine Rule

Heron’s Formula can also be easily solved using the Cosine Rule. Now for any triangle ABC if the sides of the triangle are a, b, and c and their opposite angles are, α, β, and γ....

How to Find the Area of Triangle Using Heron’s Formula?

Follow the following steps to find the area of a triangle using Heron’s formula...

Heron’s Formula for Equilateral Triangle

For an equilateral triangle, all sides are equal. Now, the semi-perimeter of the equilateral triangle is...

Heron’s Formula for Scalene Triangle

As we already know all the sides in the scalene triangle are different, i.e. no two sides are equal in the scalene triangle. We can easily find the area of the scalene triangle using Heron’s formula. For any triangle ABC where sides AB = a, BC = b, and CA = c we can find its area using,...

Heron’s Formula for Isosceles Triangle

Isosceles Triangle is a triangle that has two equal sides, their area can be easily calculated using Heron’s Formula. For any isosceles triangle, ABC where sides AB = a, and BC = a are equal and the third side is CA = b. The formula for its area is,...

Heron’s Formula for Area of Quadrilateral

Heron’s formula is used to determine the formula for the area of the quadrilateral. We can divide the quadrilateral into two separate triangles using any one of its diagonals and then the area of the two separate triangles is calculated using the Heron’s Formula....

Applications of Heron’s Formula

Heron’s formula has various applications and some of the important applications of Heron’s Formula are,...

Area of Polygon using Heron’s Formula

We can also find the area of the polygon using Heron’s Formula. A polygon is a figure formed by joining n straight lines. Its area is calculated using Heron’s Formula by using the steps discussed below,...

Heron’s Formula Class 9

Heron’s Formula is a very valuable mathematical tool introduced in Class 9, to help students calculate the area of a triangle when the lengths of all three sides are known. This formula eliminates the need for height, making it especially useful for cases where the height is difficult to determine....

Heron’s Formula Examples

Example 1: Calculate the area of a triangle whose lengths of sides a, b, and c are 14cm,13cm, and 15 cm respectively....

Summary – Heron’s Formula

Heron’s Formula provides a straightforward method to determine the area of a triangle when the lengths of all three sides are known. Named after the ancient Greek mathematician Hero of Alexandria, the formula states that the area of a triangle with side lengths a, b, and c can be calculated using the semi-perimeter s of the triangle, given by s = \frac{a + b + c}{2} The formula itself is expressed as A = \sqrt{s(s – a)(s – b)(s – c)}. Its simplicity and universality make Heron’s Formula applicable to all types of triangles, whether scalene, isosceles, or equilateral, making it a valuable tool in various fields such as geometry, engineering, architecture, and physics....

Heron’s Formula – FAQs

What is Heron’s Formula?...