function updateFields() {
var shape = document.getElementById("shapeSelect").value;
document.getElementById("rectangleInputs").style.display = (shape === "rectangle") ? "block" : "none";
document.getElementById("squareInputs").style.display = (shape === "square") ? "block" : "none";
document.getElementById("circleInputs").style.display = (shape === "circle") ? "block" : "none";
document.getElementById("triangleInputs").style.display = (shape === "triangle") ? "block" : "none";
document.getElementById("resultArea").style.display = "none";
}
function calculatePerimeter() {
var shape = document.getElementById("shapeSelect").value;
var perimeter = 0;
var formula = "";
var isValid = true;
if (shape === "rectangle") {
var l = parseFloat(document.getElementById("rectLength").value);
var w = parseFloat(document.getElementById("rectWidth").value);
if (isNaN(l) || isNaN(w) || l <= 0 || w <= 0) {
isValid = false;
} else {
perimeter = 2 * (l + w);
formula = "Formula: P = 2 × (Length + Width) = 2 × (" + l + " + " + w + ")";
}
} else if (shape === "square") {
var s = parseFloat(document.getElementById("squareSide").value);
if (isNaN(s) || s <= 0) {
isValid = false;
} else {
perimeter = 4 * s;
formula = "Formula: P = 4 × Side = 4 × " + s;
}
} else if (shape === "circle") {
var r = parseFloat(document.getElementById("circleRadius").value);
if (isNaN(r) || r <= 0) {
isValid = false;
} else {
perimeter = 2 * Math.PI * r;
formula = "Formula: C = 2 × π × r = 2 × 3.14159 × " + r;
}
} else if (shape === "triangle") {
var a = parseFloat(document.getElementById("triA").value);
var b = parseFloat(document.getElementById("triB").value);
var c = parseFloat(document.getElementById("triC").value);
if (isNaN(a) || isNaN(b) || isNaN(c) || a <= 0 || b <= 0 || c <= 0) {
isValid = false;
} else if ((a + b <= c) || (a + c <= b) || (b + c <= a)) {
alert("The sum of any two sides must be greater than the third side.");
return;
} else {
perimeter = a + b + c;
formula = "Formula: P = a + b + c = " + a + " + " + b + " + " + c;
}
}
if (!isValid) {
alert("Please enter valid positive numbers for all fields.");
return;
}
document.getElementById("perimeterOutput").innerText = "Perimeter: " + perimeter.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + " units";
document.getElementById("formulaUsed").innerText = formula;
document.getElementById("resultArea").style.display = "block";
}
How to Calculate a Perimeter: A Complete Guide
In geometry, the perimeter is the total distance around the outside of a two-dimensional shape. Understanding how to calculate it is essential for various real-world applications, from fencing a backyard to framing a picture or measuring a jogging track.
Common Perimeter Formulas
The method for finding the perimeter depends entirely on the shape you are measuring. Here are the most common formulas:
Rectangle: Since opposite sides are equal, you add the length and width together and multiply by two. P = 2(l + w)
Square: A square has four equal sides. Simply multiply the length of one side by four. P = 4s
Triangle: Add the lengths of all three sides together. P = a + b + c
Circle (Circumference): While called "circumference," it is the circle's perimeter. Multiply the radius by two and then by Pi (approximately 3.14159). C = 2πr
Real-World Example: Fencing a Garden
Suppose you have a rectangular garden that is 12 meters long and 8 meters wide. To find out how much fencing material you need to buy:
Identify the length (12) and the width (8).
Apply the rectangle formula: P = 2 × (12 + 8).
Add the numbers inside the parentheses: 12 + 8 = 20.
Multiply by two: 20 × 2 = 40.
Result: You need 40 meters of fencing.
Frequently Asked Questions
What unit is used for perimeter? Perimeter is a linear measurement, so it is measured in standard units of length such as inches, centimeters, feet, or meters (unlike area, which is measured in square units).
How do I find the perimeter of an irregular shape? For irregular polygons, simply measure every exterior side and add them all together. The "sum of all sides" rule applies to any polygon.
Is perimeter the same as area? No. Perimeter is the distance around the shape, while area is the measurement of the space inside the shape.