Calculating the area of a triangle using its three sides in JavaScript

In the realm of computational geometry, the ability to accurately calculate the area of a triangle based on its three sides is of paramount importance. JavaScript, a versatile programming language, offers developers the means to perform this complex mathematical task with precision. While the process may seem daunting at first, mastering the art of calculating the area of a triangle using its three sides in JavaScript is a testament to a developer's prowess in numerical algorithms and mathematical manipulation. In this enlightening article, we will embark on a journey through the intricacies of computational geometry, exploring a step-by-step approach to effectively determine the area of a triangle by leveraging the power of JavaScript. By delving into the lesser-known depths of JavaScript's mathematical capabilities, developers can unlock a world of possibilities and enhance their understanding of geometric computations.

Problem Statement

Develop a JavaScript function capable of accurately determining the area of a triangle, solely based on the measurements of its three distinct sides. Employing lesser-known linguistic elements, craft an informative problem statement along with a representative sample input and output.

Sample Input −

Side A: 3 units
Side B: 4 units
Side C: 5 units

Sample Output −

Area: 6

Approach

In this article, we are going to see a number of different ways to solve the above problem statement in JavaScript −

• Using Heron’s Formula

• Using Law of Cosines

Method 1: Using Heron’s Formula

To calculate the area of a triangle, first find the semi-perimeter by adding the lengths of all three sides and dividing the sum by 2. Then, apply Heron's formula, which states that the area is equal to the square root of the product of the semi-perimeter and the differences between the semi-perimeter and each side length. Finally, return the calculated area.

Example

The calculateArea function takes three parameters representing the triangle's side lengths. It calculates the semi-perimeter by adding the sides and dividing by 2. Using Heron's formula, it computes the area using the semi-perimeter and the differences between the semi-perimeter and each side. The function returns the calculated area. In the example usage, we define the side lengths and call calculateArea. The resulting area is stored in a variable and printed to the console.

function calculateArea(side1, side2, side3) {
   // Calculate the semi-perimeter
   const s = (side1 + side2 + side3) / 2;

   // Calculate the area using Heron's formula
   const area = Math.sqrt(s * (s - side1) * (s - side2) * (s - side3));
   return area;
}

// Example usage
const side1 = 3;
const side2 = 4;
const side3 = 5;
const area = calculateArea(side1, side2, side3);
console.log("Area:", area);

Output

The following is the console output −

Area: 6

Method 2: Using Law of Cosines

To calculate the angles of a triangle, the Law of Cosines is applied using the inverse cosine function (Math.acos) and the corresponding formula. Once the angles are obtained, the area of the triangle can be calculated using the formula: area = (1/2) * a * b * sin(C), where a and b represent two sides of the triangle, and C denotes the angle opposite to side C. Finally, the calculated area is returned.

Example

The calculateArea function takes side1, side2, and side3 as parameters, representing the triangle's side lengths. Inside the function, the angles are calculated using the cosine rule. Angle A is obtained using Math.acos of ((side2 * side2 + side3 * side3 - side1 * side1) / (2 * side2 * side3)), Angle B is calculated similarly, and Angle C is derived by subtracting the sum of A and B from Math.PI. The area is then calculated as (1 / 2) * side1 * side2 * Math.sin(angleC), where side1 and side2 are two sides, and angleC is the angle opposite to side C. The function returns the calculated area. In the example usage, side1, side2, and side3 are defined, and the calculateArea function is called with these side lengths. The resulting area is stored in the area variable and printed to the console.

function calculateArea(side1, side2, side3) {
   // Calculate the angles using the cosine rule
   const angleA = Math.acos((side2 * side2 + side3 * side3 - side1 * side1) / (2 * side2 * side3));
   const angleB = Math.acos((side1 * side1 + side3 * side3 - side2 * side2) / (2 * side1 * side3));
   const angleC = Math.PI - angleA - angleB;

   // Calculate the area using the formula: area = (1/2) * a * b * sin(C)
   const area = (1 / 2) * side1 * side2 * Math.sin(angleC);

   return area;
}
 
// Example usage
const side1 = 3;
const side2 = 4;
const side3 = 5;
const area = calculateArea(side1, side2, side3);
console.log("Area:", area);

Output

The following is the console output −

Area: 6

Conclusion

In culmination, the computation of a triangle's area based on its three sides using JavaScript provides a felicitous solution for developers seeking a versatile mathematical tool. By harnessing this method, programmers can accurately ascertain the area of a triangle, even in cases where only the side lengths are known. While the utilization of this approach may be esoteric to some, its inclusion in the repertoire of JavaScript functionalities expands the realm of possibilities for geometric calculations in web development. In conclusion, the implementation of this algorithmic technique augments the precision and versatility of JavaScript applications, contributing to a more erudite and comprehensive programming experience.