function toggleMethod() {
var method = document.getElementById("calcMethod").value;
var divBase = document.getElementById("methodBaseHeight");
var divHeron = document.getElementById("methodHeron");
var resultDiv = document.getElementById("triangleResult");
resultDiv.style.display = "none";
if (method === "baseHeight") {
divBase.style.display = "block";
divHeron.style.display = "none";
} else {
divBase.style.display = "none";
divHeron.style.display = "block";
}
}
function calculateByBase() {
var b = parseFloat(document.getElementById("baseValue").value);
var h = parseFloat(document.getElementById("heightValue").value);
var display = document.getElementById("triangleResult");
var output = document.getElementById("resultValue");
if (isNaN(b) || isNaN(h) || b <= 0 || h <= 0) {
alert("Please enter valid positive numbers for base and height.");
return;
}
var area = 0.5 * b * h;
output.innerHTML = area.toLocaleString(undefined, {maximumFractionDigits: 4}) + " units²";
display.style.display = "block";
}
function calculateBySides() {
var a = parseFloat(document.getElementById("sideA").value);
var b = parseFloat(document.getElementById("sideB").value);
var c = parseFloat(document.getElementById("sideC").value);
var display = document.getElementById("triangleResult");
var output = document.getElementById("resultValue");
if (isNaN(a) || isNaN(b) || isNaN(c) || a <= 0 || b <= 0 || c <= 0) {
alert("Please enter valid positive numbers for all sides.");
return;
}
if ((a + b <= c) || (a + c <= b) || (b + c <= a)) {
alert("Invalid Triangle: The sum of any two sides must be greater than the third side.");
return;
}
var s = (a + b + c) / 2;
var area = Math.sqrt(s * (s – a) * (s – b) * (s – c));
output.innerHTML = area.toLocaleString(undefined, {maximumFractionDigits: 4}) + " units²";
display.style.display = "block";
}
How to Calculate the Area of a Triangle
The area of a triangle represents the total space enclosed within its three boundaries. Whether you are a student solving geometry problems, an architect planning a floor layout, or a DIY enthusiast measuring a roof, knowing how to calculate triangle area is essential.
The Standard Formula: Base and Height
The most common way to find the area is using the base and the vertical height. The formula is:
Area = ½ × Base × Height
Example: If you have a triangle with a base of 10 cm and a height of 5 cm, the calculation would be:
0.5 × 10 × 5 = 25 cm².
Heron's Formula: When You Only Know the Sides
If you don't know the vertical height but you have the lengths of all three sides (a, b, and c), 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)]
Frequently Asked Questions
What units are used for triangle area?
The area is always expressed in square units, such as square inches (in²), square centimeters (cm²), or square meters (m²).
Can any three lengths form a triangle?
No. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides must be strictly greater than the length of the third side. If this condition isn't met, the lines cannot meet to form a closed triangle.
How do I find the height of a triangle?
The height (or altitude) is the perpendicular line segment from a vertex to the opposite side (the base). In a right-angled triangle, if one leg is the base, the other leg is the height.