Calculating the area of a triangle is a fundamental skill in geometry. Depending on the information you have available, there are two primary ways to find the total space inside a triangle: using the base and height or using the lengths of all three sides.
Method 1: Base and Height (The Standard Formula)
If you know the length of one side (the base) and the perpendicular distance from that side to the opposite vertex (the height), the formula is straightforward:
Area = (Base × Height) / 2
Example: If a triangle has a base of 10 cm and a height of 5 cm, the area is (10 × 5) / 2 = 25 cm².
Method 2: Heron's Formula (Using Three Sides)
When you know the lengths of all three sides but not the height, you use Heron's Formula. First, calculate the semi-perimeter (s):
s = (Side A + Side B + Side C) / 2
Then apply the area formula:
Area = √[s × (s – A) × (s – B) × (s – C)]
Important Rules for Triangles
The Triangle Inequality Theorem: For a triangle to be valid, the sum of any two sides must be strictly greater than the third side (A + B > C).
Units: Always ensure your measurements are in the same units (e.g., all in inches or all in centimeters) before calculating.
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 toggleInputs() {
var method = document.getElementById("calcMethod").value;
var bhDiv = document.getElementById("baseHeightInputs");
var tsDiv = document.getElementById("threeSidesInputs");
var resultDiv = document.getElementById("triangleResult");
var errorDiv = document.getElementById("errorMessage");
resultDiv.style.display = "none";
errorDiv.style.display = "none";
if (method === "baseHeight") {
bhDiv.style.display = "block";
tsDiv.style.display = "none";
} else {
bhDiv.style.display = "none";
tsDiv.style.display = "block";
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}
function calculateTriangle() {
var method = document.getElementById("calcMethod").value;
var area = 0;
var perimeter = 0;
var isValid = false;
var resultDiv = document.getElementById("triangleResult");
var errorDiv = document.getElementById("errorMessage");
var areaOutput = document.getElementById("areaOutput");
var perimeterOutput = document.getElementById("perimeterOutput");
resultDiv.style.display = "none";
errorDiv.style.display = "none";
if (method === "baseHeight") {
var b = parseFloat(document.getElementById("baseInput").value);
var h = parseFloat(document.getElementById("heightInput").value);
if (isNaN(b) || isNaN(h) || b <= 0 || h <= 0) {
errorDiv.innerText = "Please enter valid positive numbers for base and height.";
errorDiv.style.display = "block";
return;
}
area = 0.5 * b * h;
areaOutput.innerText = "Calculated Area: " + area.toFixed(2);
perimeterOutput.innerText = "Note: Perimeter cannot be calculated from base and height alone without the side lengths.";
isValid = true;
} else {
var s1 = parseFloat(document.getElementById("sideA").value);
var s2 = parseFloat(document.getElementById("sideB").value);
var s3 = parseFloat(document.getElementById("sideC").value);
if (isNaN(s1) || isNaN(s2) || isNaN(s3) || s1 <= 0 || s2 <= 0 || s3 s3) && (s1 + s3 > s2) && (s2 + s3 > s1)) {
var s = (s1 + s2 + s3) / 2;
area = Math.sqrt(s * (s – s1) * (s – s2) * (s – s3));
perimeter = s1 + s2 + s3;
areaOutput.innerText = "Calculated Area: " + area.toFixed(2);
perimeterOutput.innerText = "Total Perimeter: " + perimeter.toFixed(2);
isValid = true;
} else {
errorDiv.innerText = "Invalid Triangle: The sum of any two sides must be greater than the third side.";
errorDiv.style.display = "block";
return;
}
}
if (isValid) {
resultDiv.style.display = "block";
}
}