How to Calculate Area of the Triangle

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Triangle Area Calculator

Calculate the area of any triangle using base and height or side lengths.

Calculated Result:

How to Calculate Area of a Triangle

Finding the area of a triangle is a fundamental skill in geometry. Depending on the information you have available (base/height vs. all three side lengths), there are different formulas you can use.

1. The Standard Formula (Base and Height)

This is the most common way to calculate area. If you know the length of one side (the base) and the perpendicular distance from that side to the opposite vertex (the height), use this formula:

Area = ½ × Base × Height

Example: If a triangle has a base of 10cm and a height of 6cm, the calculation is:
0.5 × 10 × 6 = 30cm².

2. Heron's Formula (Three Sides)

If you know the lengths of all three sides (a, b, and c) but not the height, you use Heron's Formula. First, calculate the semi-perimeter (s):

s = (a + b + c) / 2

Then, apply the area formula:

Area = √[s(s – a)(s – b)(s – c)]

Example: For sides 3, 4, and 5:
s = (3+4+5)/2 = 6.
Area = √[6(6-3)(6-4)(6-5)] = √[6 × 3 × 2 × 1] = √36 = 6 units².

Important Geometric Rules

  • The Triangle Inequality: To form a valid triangle, the sum of any two sides must be greater than the third side. If this isn't true, the area cannot be calculated.
  • Units: Always ensure your measurements are in the same unit (e.g., all centimeters or all meters) before calculating. The resulting area will be in square units.
  • Right-Angled Triangles: For right triangles, the base and height are simply the two sides meeting at the 90-degree angle.
var currentMethod = 'bh'; function switchMethod(method) { currentMethod = method; var bhDiv = document.getElementById('methodBH'); var sidesDiv = document.getElementById('methodSides'); var btn1 = document.getElementById('btnMethod1'); var btn2 = document.getElementById('btnMethod2'); var resultBox = document.getElementById('resultContainer'); var errorBox = document.getElementById('calcError'); resultBox.style.display = 'none'; errorBox.style.display = 'none'; if (method === 'bh') { bhDiv.style.display = 'block'; sidesDiv.style.display = 'none'; btn1.classList.add('active'); btn2.classList.remove('active'); } else { bhDiv.style.display = 'none'; sidesDiv.style.display = 'block'; btn1.classList.remove('active'); btn2.classList.add('active'); } } function performCalculation() { var resultText = document.getElementById('resultText'); var calcSteps = document.getElementById('calcSteps'); var resultBox = document.getElementById('resultContainer'); var errorBox = document.getElementById('calcError'); errorBox.style.display = 'none'; resultBox.style.display = 'none'; if (currentMethod === 'bh') { var b = parseFloat(document.getElementById('triBase').value); var h = parseFloat(document.getElementById('triHeight').value); if (isNaN(b) || isNaN(h) || b <= 0 || h <= 0) { showError("Please enter valid positive numbers for base and height."); return; } var area = 0.5 * b * h; resultText.innerText = area.toLocaleString() + " square units"; calcSteps.innerText = "Calculation: (0.5 × " + b + " × " + h + ") = " + area; resultBox.style.display = 'block'; } else { var a = parseFloat(document.getElementById('sideA').value); var b = parseFloat(document.getElementById('sideB').value); var c = parseFloat(document.getElementById('sideC').value); if (isNaN(a) || isNaN(b) || isNaN(c) || a <= 0 || b <= 0 || c <= 0) { showError("Please enter valid positive numbers for all three sides."); return; } // Check triangle inequality if ((a + b <= c) || (a + c <= b) || (b + c <= a)) { showError("Invalid Triangle: The sum of any two sides must be greater than the third side."); return; } var s = (a + b + c) / 2; var areaSquared = s * (s – a) * (s – b) * (s – c); var area = Math.sqrt(areaSquared); resultText.innerText = area.toFixed(4).replace(/\.?0+$/, "") + " square units"; calcSteps.innerText = "Semi-perimeter (s) = " + s + ". Heron's Formula applied."; resultBox.style.display = 'block'; } } function showError(msg) { var errorBox = document.getElementById('calcError'); errorBox.innerText = msg; errorBox.style.display = 'block'; }

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