Select the type of triangle and provide the known values.
Right Triangle (Legs)
General Triangle (Base & Height)
Triangle (Three Sides – Heron's Formula)
Results will appear here.
Understanding Triangle Calculations
Triangles are fundamental geometric shapes with three sides and three angles. Calculating their area and perimeter is essential in various fields, including construction, engineering, design, and mathematics.
Area Formulas:
Right Triangle (using legs): If you know the lengths of the two legs (the sides forming the right angle), the area is calculated as: Area = 0.5 * legA * legB.
General Triangle (using base and height): For any triangle, if you know the length of one side (the base) and the perpendicular height from the opposite vertex to that base, the area is: Area = 0.5 * base * height.
Triangle (using three sides – Heron's Formula): If you only know the lengths of all three sides (a, b, c), you can use Heron's formula. First, calculate the semi-perimeter (s): s = (a + b + c) / 2. Then, the area is: Area = sqrt(s * (s - a) * (s - b) * (s - c)).
Perimeter Formula:
The perimeter of any triangle is simply the sum of the lengths of its three sides:
Perimeter = sideA + sideB + sideC
For right triangles, the hypotenuse can be found using the Pythagorean theorem: hypotenuse = sqrt(legA^2 + legB^2). The perimeter would then be legA + legB + hypotenuse.
Use Cases:
Construction & Architecture: Calculating the area of triangular roof sections or triangular plots of land.
Engineering: Determining forces and stresses in triangular structures.
Graphic Design & Game Development: Defining shapes and calculating surface areas for rendering.
Navigation: Using triangulation to determine position.
Mathematics Education: Practicing geometric principles and formulas.
function updateInputs() {
var type = document.getElementById("triangleType").value;
document.getElementById("rightTriangleInputs").style.display = (type === "right") ? "block" : "none";
document.getElementById("generalTriangleInputs").style.display = (type === "general") ? "block" : "none";
document.getElementById("sidesTriangleInputs").style.display = (type === "sides") ? "block" : "none";
document.getElementById("result").innerHTML = "Results will appear here."; // Clear previous results
}
function getNumericValue(id) {
var value = parseFloat(document.getElementById(id).value);
return isNaN(value) || value <= 0 ? null : value;
}
function calculateArea() {
var type = document.getElementById("triangleType").value;
var area = null;
var resultHtml = "";
if (type === "right") {
var legA = getNumericValue("legA");
var legB = getNumericValue("legB");
if (legA !== null && legB !== null) {
area = 0.5 * legA * legB;
resultHtml = "Calculated Area: " + area.toFixed(4) + " square units";
} else {
resultHtml = "Please enter valid positive numbers for both legs.";
}
} else if (type === "general") {
var base = getNumericValue("base");
var height = getNumericValue("height");
if (base !== null && height !== null) {
area = 0.5 * base * height;
resultHtml = "Calculated Area: " + area.toFixed(4) + " square units";
} else {
resultHtml = "Please enter valid positive numbers for base and height.";
}
} else if (type === "sides") {
var sideA = getNumericValue("sideA");
var sideB = getNumericValue("sideB");
var sideC = getNumericValue("sideC");
if (sideA !== null && sideB !== null && sideC !== null) {
// Check triangle inequality theorem
if ((sideA + sideB > sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA)) {
var s = (sideA + sideB + sideC) / 2;
var areaSquared = s * (s – sideA) * (s – sideB) * (s – sideC);
if (areaSquared >= 0) { // Ensure non-negative value before sqrt
area = Math.sqrt(areaSquared);
resultHtml = "Calculated Area: " + area.toFixed(4) + " square units";
} else {
resultHtml = "The provided side lengths do not form a valid triangle.";
}
} else {
resultHtml = "The provided side lengths do not form a valid triangle (Triangle Inequality Theorem violated).";
}
} else {
resultHtml = "Please enter valid positive numbers for all three sides.";
}
}
document.getElementById("result").innerHTML = resultHtml;
}
function calculatePerimeter() {
var perimeter = null;
var perimeterHtml = "";
var type = document.getElementById("triangleType").value;
if (type === "right") {
var legA = getNumericValue("legA");
var legB = getNumericValue("legB");
if (legA !== null && legB !== null) {
var hypotenuse = Math.sqrt(Math.pow(legA, 2) + Math.pow(legB, 2));
perimeter = legA + legB + hypotenuse;
perimeterHtml = "Calculated Perimeter: " + perimeter.toFixed(4) + " units (Hypotenuse: " + hypotenuse.toFixed(4) + ")";
} else {
perimeterHtml = "Please enter valid positive numbers for both legs.";
}
} else { // General and Sides triangle types use the same perimeter calculation
var sideA = getNumericValue("sideA");
var sideB = getNumericValue("sideB");
var sideC = getNumericValue("sideC");
// If general triangle inputs are visible, use them for perimeter
if (document.getElementById("generalTriangleInputs").style.display !== "none") {
sideA = getNumericValue("base"); // For perimeter, base is just one side
sideB = getNumericValue("sideB") !== null ? getNumericValue("sideB") : 0; // Placeholder if not defined
sideC = getNumericValue("sideC") !== null ? getNumericValue("sideC") : 0; // Placeholder if not defined
// This part is tricky as general triangle inputs only show base and height.
// For perimeter, we need 3 sides. Let's assume if general is selected, we can't calculate perimeter without more info.
// However, the 'sides' input group is always available and hidden/shown.
// Let's prioritize the 'sides' inputs if they are valid, otherwise fall back to general if possible.
if (sideA !== null && sideB !== null && sideC !== null) {
perimeter = sideA + sideB + sideC;
perimeterHtml = "Calculated Perimeter: " + perimeter.toFixed(4) + " units";
} else {
perimeterHtml = "Please enter valid positive numbers for all three sides to calculate perimeter.";
}
} else if (sideA !== null && sideB !== null && sideC !== null) { // Use sides inputs
perimeter = sideA + sideB + sideC;
perimeterHtml = "Calculated Perimeter: " + perimeter.toFixed(4) + " units";
} else {
perimeterHtml = "Please enter valid positive numbers for all three sides to calculate perimeter.";
}
}
document.getElementById("result").innerHTML = perimeterHtml;
}
// Initialize the view based on the default selection
document.addEventListener('DOMContentLoaded', updateInputs);