How to Calculate Triangle Area

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Triangle Area Calculator

Method 1: Using Base and Height

The most common way to find the area of a triangle.

Method 2: Heron's Formula (3 Sides)

Useful when you know the lengths of all three sides (a, b, and c).

How to Calculate Triangle Area

Calculating the area of a triangle is a fundamental skill in geometry. Whether you are working on a construction project, solving a math problem, or landscaping your garden, knowing how much surface area a triangular space occupies is essential. There are two primary ways to calculate this depending on what information you have available.

Method 1: The Standard Formula (Base & Height)

If you know the length of one side (the base) and the perpendicular distance from that base to the opposite corner (the height), you use the most common triangle formula:

Formula: Area = ½ × Base × Height

Example: Suppose you have a triangle with a base of 12 cm and a vertical height of 8 cm.

  • Area = 0.5 × 12 × 8
  • Area = 6 × 8
  • Area = 48 square centimeters (cm²)

Method 2: Heron's Formula (All Three Sides)

If you don't know the height but you know the length of all three sides (a, b, and c), you use Heron's Formula. First, calculate the semi-perimeter (s), which is half of the triangle's perimeter:

Semi-perimeter (s) = (a + b + c) / 2
Area = √[s × (s – a) × (s – b) × (s – c)]

Example: A triangle with sides 5, 6, and 7 units.

  1. s = (5 + 6 + 7) / 2 = 9
  2. Area = √[9 × (9-5) × (9-6) × (9-7)]
  3. Area = √[9 × 4 × 3 × 2] = √216
  4. Area ≈ 14.7 square units

Important Rules to Remember

  • Units: Always ensure your measurements are in the same unit (e.g., all inches or all centimeters) before calculating. The result will be in square units.
  • Triangle Inequality: For Heron's Formula to work, the sum of any two sides must be greater than the third side (a + b > c). If this isn't true, a triangle cannot physically exist.
  • Right Triangles: In a right-angled triangle, the two sides meeting at the 90-degree angle can serve as the base and the height.
function calculateByBaseHeight() { var base = parseFloat(document.getElementById('triBase').value); var height = parseFloat(document.getElementById('triHeight').value); var resultDiv = document.getElementById('bhResult'); if (isNaN(base) || isNaN(height) || base <= 0 || height <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for both fields."; resultDiv.style.color = "#e74c3c"; return; } var area = 0.5 * base * height; resultDiv.innerHTML = "Resulting Area: " + area.toFixed(2); resultDiv.style.color = "#27ae60"; } function calculateByHeron() { var a = parseFloat(document.getElementById('sideA').value); var b = parseFloat(document.getElementById('sideB').value); var c = parseFloat(document.getElementById('sideC').value); var resultDiv = document.getElementById('heronResult'); if (isNaN(a) || isNaN(b) || isNaN(c) || a <= 0 || b <= 0 || c <= 0) { resultDiv.innerHTML = "Please enter valid positive side lengths."; resultDiv.style.color = "#e74c3c"; return; } // Check triangle inequality theorem if ((a + b <= c) || (a + c <= b) || (b + c <= a)) { resultDiv.innerHTML = "Invalid sides: The sum of two sides must be greater than the third."; resultDiv.style.color = "#e74c3c"; return; } var s = (a + b + c) / 2; var areaValue = Math.sqrt(s * (s – a) * (s – b) * (s – c)); resultDiv.innerHTML = "Resulting Area: " + areaValue.toFixed(2); resultDiv.style.color = "#27ae60"; }

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