Triangle Area Calculator with 3 Sides

Triangle Area Calculator (3 Sides)

function calculateTriangleArea() { var sideA = parseFloat(document.getElementById('sideA').value); var sideB = parseFloat(document.getElementById('sideB').value); var sideC = parseFloat(document.getElementById('sideC').value); var resultDiv = document.getElementById('result'); if (isNaN(sideA) || isNaN(sideB) || isNaN(sideC) || sideA <= 0 || sideB <= 0 || sideC <= 0) { resultDiv.innerHTML = 'Please enter valid positive numbers for all side lengths.'; return; } // Triangle Inequality Theorem check if (!((sideA + sideB > sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA))) { resultDiv.innerHTML = 'These side lengths cannot form a valid triangle (Triangle Inequality Theorem).'; return; } // Heron's Formula var s = (sideA + sideB + sideC) / 2; // Semi-perimeter var area = Math.sqrt(s * (s – sideA) * (s – sideB) * (s – sideC)); if (isNaN(area) || area <= 0) { // Check for cases where area might be 0 or NaN due to floating point inaccuracies for degenerate triangles resultDiv.innerHTML = 'The provided side lengths form a degenerate triangle or an invalid configuration.'; } else { resultDiv.innerHTML = 'The area of the triangle is: ' + area.toFixed(4) + ' square units.'; } }

Understanding the Triangle Area Calculator (3 Sides)

Calculating the area of a triangle is a fundamental concept in geometry, with applications ranging from construction and engineering to art and design. While the most common formula for a triangle's area involves its base and height (Area = 0.5 * base * height), this isn't always practical if you only know the lengths of its three sides.

What is Heron's Formula?

When you have the lengths of all three sides of a triangle (let's call them 'a', 'b', and 'c'), you can use a powerful formula known as Heron's Formula to find its area. This formula is particularly useful because it doesn't require knowing any angles or the perpendicular height of the triangle.

How Heron's Formula Works

Heron's Formula involves two main steps:

1. Calculate the Semi-Perimeter (s): The semi-perimeter is half the perimeter of the triangle.
   s = (a + b + c) / 2
2. Calculate the Area: Once you have the semi-perimeter, you can plug it into the main formula:
   Area = √(s * (s - a) * (s - b) * (s - c))

The Triangle Inequality Theorem

Before calculating the area, it's crucial to ensure that the given side lengths can actually form a triangle. This is determined by the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this condition is not met, the sides cannot form a valid triangle.

• a + b > c
• a + c > b
• b + c > a

Example Calculation

Let's say you have a triangle with sides of length 3, 4, and 5 units. This is a classic right-angled triangle.

1. Check Triangle Inequality:
   • 3 + 4 > 5 (7 > 5 – True)
   • 3 + 5 > 4 (8 > 4 – True)
   • 4 + 5 > 3 (9 > 3 – True)
   Since all conditions are met, these sides can form a triangle.
2. Calculate Semi-Perimeter (s):
   s = (3 + 4 + 5) / 2 = 12 / 2 = 6
3. Calculate Area:
   Area = √(6 * (6 - 3) * (6 - 4) * (6 - 5))
Area = √(6 * 3 * 2 * 1)
Area = √(36)
Area = 6 square units

This calculator uses Heron's formula to quickly and accurately determine the area of any triangle, given only the lengths of its three sides, while also validating if a triangle can actually be formed.