Find Area of Triangle with 3 Sides Calculator

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. The sum of any two sides must be greater than the third side.'; return; } // Calculate semi-perimeter (s) var s = (sideA + sideB + sideC) / 2; // Calculate area using Heron's formula var areaSquared = s * (s – sideA) * (s – sideB) * (s – sideC); // Handle potential floating point inaccuracies that might lead to a tiny negative number // under the square root for very degenerate triangles or specific floating point values. if (areaSquared < 0) { areaSquared = 0; } var area = Math.sqrt(areaSquared); resultDiv.innerHTML = 'The area of the triangle is: ' + area.toFixed(4) + ' square units'; }

Understanding the Area of a Triangle with Three Sides

Calculating the area of a triangle is a fundamental concept in geometry. While you might be familiar with the formula involving base and height (Area = 0.5 * base * height), what if you only know the lengths of all three sides? This is where Heron's formula comes to the rescue.

What is Heron's Formula?

Heron's formula, named after Hero of Alexandria, provides a way to calculate the area of a triangle when the lengths of all three sides are known. It's particularly useful when the height of the triangle is not readily available or difficult to determine.

The formula is as follows:

Area = √[s * (s – a) * (s – b) * (s – c)]

Where:

• a, b, and c are the lengths of the three sides of the triangle.
• s is the "semi-perimeter" of the triangle, which is half of its perimeter. It's calculated as: s = (a + b + c) / 2.

How to Use the Calculator

Our Triangle Area Calculator simplifies this process for you. Simply follow these steps:

1. Enter Side A Length: Input the length of the first side of your triangle into the "Side A Length" field.
2. Enter Side B Length: Input the length of the second side into the "Side B Length" field.
3. Enter Side C Length: Input the length of the third side into the "Side C Length" field.
4. Click "Calculate Area": The calculator will instantly compute and display the area of your triangle in "square units".

The calculator also includes a crucial validation: it checks if the entered side lengths can actually form a triangle. This is based on 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.

Example Calculation

Let's say you have a triangle with the following side lengths:

• Side A = 3 units
• Side B = 4 units
• Side C = 5 units

Here's how Heron's formula would calculate the area:

1. Calculate the semi-perimeter (s):
   s = (3 + 4 + 5) / 2 = 12 / 2 = 6
2. Apply Heron's Formula:
   Area = √[6 * (6 - 3) * (6 - 4) * (6 - 5)]
Area = √[6 * 3 * 2 * 1]
Area = √[36]
Area = 6

So, the area of a triangle with sides 3, 4, and 5 units is 6 square units. This is a classic example of a right-angled triangle, where you could also use (0.5 * base * height) = (0.5 * 3 * 4) = 6.

Use this calculator to quickly and accurately find the area of any triangle, given its three side lengths!