Your comprehensive tool for calculating geometric areas
Calculate Geometric Area
Square
Rectangle
Triangle
Circle
Trapezoid
Parallelogram
Ellipse
Choose the geometric shape you want to calculate the area for.
Calculated Area
—
Square Units
Formula Used
Select a figure type to see the formula.
Key Intermediate Values
No intermediate values yet.
Area of a Figure Calculator: Understanding Geometric Measurements
Welcome to our advanced **Area of a Figure Calculator**, a sophisticated yet user-friendly tool designed to simplify the calculation of geometric areas for a wide array of shapes. Whether you're a student grappling with geometry homework, a professional involved in construction, design, or land surveying, or simply a curious individual, this calculator provides precise results instantly. Understanding how to calculate the area of a figure is fundamental in many practical applications, from determining the amount of paint needed for a wall to calculating the land size for property development. Our calculator aims to demystify these calculations, offering clear formulas, detailed explanations, and real-world context to enhance your understanding of the **area of a figure calculator**.
The Significance of Area Calculations
Area is a measure of the two-dimensional space occupied by a shape. It's a critical concept in mathematics and its applications. For instance, knowing the area of a room helps in carpeting or tiling calculations, while understanding the area of a plot of land is essential for real estate transactions and urban planning. This **area of a figure calculator** is built to handle common geometric shapes, ensuring accuracy and speed, making it an indispensable resource for anyone needing to perform these calculations efficiently.
What is Area of a Figure?
The "area of a figure" refers to the total amount of two-dimensional space enclosed within the boundaries of a specific geometric shape. It's a fundamental concept in geometry that quantifies the extent of a surface. Unlike length, which measures one dimension, or volume, which measures three dimensions, area specifically deals with the plane occupied by a figure.
Who should use it: This calculator is invaluable for students learning geometry, architects and designers planning spaces, engineers calculating material requirements, construction workers estimating material quantities (like paint, flooring, or concrete), real estate professionals assessing property sizes, and hobbyists involved in crafts or DIY projects that require precise measurements.
Common misconceptions: A frequent misconception is confusing area with perimeter (the distance around the figure). Another is assuming all shapes with the same perimeter have the same area, which is only true for specific cases (e.g., squares vs. rectangles). Also, some might overlook the importance of units – area is always measured in square units (e.g., square meters, square feet).
Area of a Figure Formula and Mathematical Explanation
The calculation of area varies significantly depending on the specific geometric figure. Our **area of a figure calculator** dynamically applies the correct formula based on your selection. Below are the primary formulas and a step-by-step breakdown for common shapes:
General Approach
To calculate the area of a figure, you typically need specific linear measurements (like length, width, radius, height) and apply a well-defined mathematical formula. The result is always expressed in square units.
Key Variables in Area Calculations
Variable Name
Meaning
Unit
Typical Range
Length (l)
The longer dimension of a rectangle or parallelogram.
Units (e.g., m, ft)
Positive values
Width (w)
The shorter dimension of a rectangle or parallelogram.
Units (e.g., m, ft)
Positive values
Side (s)
The length of one side of a square.
Units (e.g., m, ft)
Positive values
Base (b)
The length of the bottom side of a triangle, trapezoid, or parallelogram.
Units (e.g., m, ft)
Positive values
Height (h)
The perpendicular distance from the base to the opposite vertex or side.
Units (e.g., m, ft)
Positive values
Radius (r)
The distance from the center of a circle to its edge.
Units (e.g., m, ft)
Positive values
Semi-major Axis (a)
Half the longest diameter of an ellipse.
Units (e.g., m, ft)
Positive values
Semi-minor Axis (b)
Half the shortest diameter of an ellipse.
Units (e.g., m, ft)
Positive values
Parallel Side 1 (b1)
Length of one of the parallel sides of a trapezoid.
Units (e.g., m, ft)
Positive values
Parallel Side 2 (b2)
Length of the other parallel side of a trapezoid.
Units (e.g., m, ft)
Positive values
π (Pi)
Mathematical constant, approximately 3.14159.
Dimensionless
Constant
Specific Formulas Implemented:
Square: Area = side * side (s²)
Rectangle: Area = length * width (l * w)
Triangle: Area = 0.5 * base * height (0.5 * b * h)
Ellipse: Area = π * semi-major axis * semi-minor axis (π * a * b)
Our **area of a figure calculator** streamlines these calculations, ensuring you get accurate results for your specific geometric problem. This involves inputting the relevant dimensions for the chosen figure, and the calculator handles the rest, providing the final area and intermediate steps.
Practical Examples (Real-World Use Cases)
Understanding the **area of a figure calculator** is best done through practical application. Here are a couple of scenarios:
Example 1: Tiling a Rectangular Room
Scenario: Sarah is renovating her kitchen and needs to tile the floor. The kitchen floor is rectangular, measuring 4 meters in length and 3 meters in width. She needs to know the area to purchase the correct amount of tiles.
Inputs:
Figure Type: Rectangle
Length: 4 meters
Width: 3 meters
Calculation using the Area of a Figure Calculator:
The calculator uses the formula: Area = Length × Width.
Intermediate Values:
Length: 4 m
Width: 3 m
Output Result:
12 square meters
Financial Interpretation: Sarah knows she needs exactly 12 square meters of tiles. She might purchase slightly more (e.g., 10-15% extra) to account for cuts and potential breakages, but the core requirement is 12 square meters. This prevents overspending or running short.
Example 2: Calculating the Size of a Circular Garden Plot
Scenario: David wants to create a circular flower garden. He has decided the garden should have a radius of 5 feet. He needs to calculate the area to determine how many plants he can fit.
Inputs:
Figure Type: Circle
Radius: 5 feet
Calculation using the Area of a Figure Calculator:
The calculator uses the formula: Area = π × radius².
Intermediate Values:
Radius: 5 ft
Radius Squared: 25 sq ft
π (Pi): Approx. 3.14159
Output Result:
78.54 square feet
Financial Interpretation: David now knows his garden plot covers approximately 78.54 square feet. This area calculation helps him plan plant spacing and purchase the appropriate number of seedlings or plants, ensuring efficient use of his garden space and budget.
How to Use This Area of a Figure Calculator
Our **Area of a Figure Calculator** is designed for simplicity and efficiency. Follow these steps:
Select Figure Type: From the dropdown menu, choose the specific geometric shape (e.g., Square, Rectangle, Circle, Triangle) for which you need to calculate the area.
Input Dimensions: Based on your selection, relevant input fields will appear. Enter the required measurements accurately. For example, for a rectangle, you'll need to input the 'Length' and 'Width'. Ensure you use consistent units (e.g., all in meters, or all in feet).
View Formula: The calculator will display the specific formula being used for your chosen figure, aiding understanding.
Calculate: Click the "Calculate Area" button.
Interpret Results: The primary result will show the calculated area in square units. Intermediate values, if applicable, will also be displayed, offering a breakdown of the calculation process.
Reset: If you need to start over or calculate for a different figure, click the "Reset" button.
Copy Results: Use the "Copy Results" button to easily share or save the calculated area and summary information.
How to interpret results: The main output is your area in square units. This value directly quantifies the surface enclosed by the figure. For practical purposes, it helps in determining quantities of materials, space allocation, or surface coverage.
Decision-making guidance: Use the calculated area to make informed decisions. For instance, if calculating paint needed for a wall, compare the area to the coverage stated on the paint can. If designing a room layout, ensure the total area of furniture does not exceed a reasonable percentage of the room's floor area.
Key Factors That Affect Area Results
While the formulas are precise, several factors can influence the practical application and interpretation of area calculations:
Accuracy of Measurements: The most crucial factor. Inaccurate input dimensions (length, width, radius, height, etc.) will directly lead to an incorrect area calculation. Precision in measuring is key for real-world applications like construction.
Units of Measurement: Always ensure consistency. Mixing units (e.g., length in meters, width in centimeters) will yield nonsensical results. The final area will be in the square of the input unit (e.g., square meters, square feet).
Shape Complexity: For irregular or composite shapes (shapes made up of multiple basic figures), the calculation becomes more complex. You might need to break down the shape into simpler components and sum their areas, or use more advanced calculus methods. Our calculator focuses on standard geometric figures.
Curved vs. Straight Edges: Figures with straight edges (polygons) have simpler area formulas compared to those with curved edges (circles, ellipses), which involve pi (π). This often requires rounding or approximation.
Dimensional Consistency: Ensure you are using the correct dimensions for the formula. For a triangle, you need the base and the perpendicular height, not just any side length. For a circle, the radius is needed, not the diameter (though diameter can be used: Area = π * (diameter/2)²).
Scale and Proportion: When dealing with scale models or plans, the area scales by the square of the linear scaling factor. Doubling the dimensions of a rectangle quadruples its area. This is crucial in design and manufacturing.
3D Objects: Remember that area applies to 2D surfaces. For 3D objects, you would calculate surface area (the sum of the areas of all faces) or volume (the space occupied). Our **area of a figure calculator** is strictly for 2D figures.
Understanding these factors ensures that the results from our **area of a figure calculator** are applied effectively and accurately in practical scenarios. This tool is a stepping stone to more complex spatial reasoning.
Frequently Asked Questions (FAQ)
Q1: What is the difference between area and perimeter?
Area measures the space enclosed within a 2D shape, while perimeter measures the total length of its boundary. Think of area as the amount of carpet needed for a room, and perimeter as the amount of baseboard trim required.
Q2: Can I calculate the area of an irregular shape with this calculator?
This calculator is designed for standard geometric figures (squares, circles, rectangles, etc.). For irregular shapes, you would typically divide the shape into simpler, standard figures, calculate each area, and sum them up, or use advanced methods like coordinate geometry or calculus.
Q3: Does the calculator handle different units (e.g., feet, meters)?
The calculator itself performs the mathematical operation. You must ensure that all your input measurements are in the same unit (e.g., all feet, all meters). The output area will be in the square of that unit (e.g., square feet, square meters).
Q4: Why is Pi (π) used in circle and ellipse calculations?
Pi is a fundamental mathematical constant representing the ratio of a circle's circumference to its diameter. It's irrational and appears in formulas for circles and ellipses because their shapes are intrinsically related to circular proportions.
Q5: What does "square units" mean in the result?
"Square units" indicates that the measurement represents an area. If your inputs were in meters, the area is in square meters (m²). If inputs were in inches, the area is in square inches (in²).
Q6: How accurate is the calculator?
The calculator uses standard mathematical formulas and floating-point arithmetic, providing high precision. Accuracy primarily depends on the precision of the input values you provide.
Q7: Can I calculate the surface area of a 3D object?
No, this calculator is strictly for 2D figures (flat shapes). Surface area calculations for 3D objects require different formulas and inputs specific to those shapes (e.g., cubes, spheres, cylinders).
Q8: What if my shape is a combination of figures, like a square with a semicircle on top?
You would need to calculate the area of each component part separately using this calculator (or appropriate formulas) and then sum the results. For example, calculate the square's area and the semicircle's area and add them together.
Related Tools and Internal Resources
Explore More Calculators and Guides:
Perimeter Calculator – Estimate the boundary length of various geometric shapes. Useful for tasks involving outlining or framing.
Volume Calculator – Calculate the space occupied by 3D objects. Essential for material estimation in construction and packaging.
Geometry Formulas Guide – A comprehensive reference for common geometric formulas, including area, perimeter, and volume.
Construction Cost Estimator – Helps estimate project costs based on dimensions and material choices, often using area calculations.
Paint Calculator – Specifically calculates the amount of paint needed for walls or ceilings based on their area.
Unit Converter – Seamlessly convert measurements between different units (e.g., meters to feet, square meters to square feet).
var currentFigureType = "square";
var figureInputs = {
"square": [
{ id: "side", label: "Side Length", type: "number", helper: "Enter the length of one side." }
],
"rectangle": [
{ id: "length", label: "Length", type: "number", helper: "Enter the length of the rectangle." },
{ id: "width", label: "Width", type: "number", helper: "Enter the width of the rectangle." }
],
"triangle": [
{ id: "base", label: "Base", type: "number", helper: "Enter the base length of the triangle." },
{ id: "height", label: "Height", type: "number", helper: "Enter the perpendicular height." }
],
"circle": [
{ id: "radius", label: "Radius", type: "number", helper: "Enter the radius from the center to the edge." }
],
"trapezoid": [
{ id: "base1", label: "Parallel Side 1", type: "number", helper: "Enter the length of the first parallel side." },
{ id: "base2", label: "Parallel Side 2", type: "number", helper: "Enter the length of the second parallel side." },
{ id: "height", label: "Height", type: "number", helper: "Enter the perpendicular height between the parallel sides." }
],
"parallelogram": [
{ id: "base", label: "Base", type: "number", helper: "Enter the base length." },
{ id: "height", label: "Height", type: "number", helper: "Enter the perpendicular height." }
],
"ellipse": [
{ id: "semiMajorAxis", label: "Semi-major Axis (a)", type: "number", helper: "Enter half the longest diameter." },
{ id: "semiMinorAxis", label: "Semi-minor Axis (b)", type: "number", helper: "Enter half the shortest diameter." }
]
};
var figureFormulas = {
"square": { formula: "Area = side²", explanation: "The area of a square is calculated by squaring the length of one of its sides." },
"rectangle": { formula: "Area = Length × Width", explanation: "The area of a rectangle is found by multiplying its length by its width." },
"triangle": { formula: "Area = 0.5 × Base × Height", explanation: "The area of a triangle is half the product of its base and its perpendicular height." },
"circle": { formula: "Area = π × Radius²", explanation: "The area of a circle is calculated using Pi (π) multiplied by the square of its radius." },
"trapezoid": { formula: "Area = 0.5 × (Base1 + Base2) × Height", explanation: "The area of a trapezoid is half the sum of its parallel bases multiplied by the perpendicular height." },
"parallelogram": { formula: "Area = Base × Height", explanation: "The area of a parallelogram is its base multiplied by its perpendicular height." },
"ellipse": { formula: "Area = π × a × b", explanation: "The area of an ellipse is Pi (π) multiplied by the product of its semi-major axis (a) and semi-minor axis (b)." }
};
function updateInputs() {
var figureTypeSelect = document.getElementById("figureType");
currentFigureType = figureTypeSelect.value;
var inputsContainer = document.getElementById("inputsContainer");
inputsContainer.innerHTML = ""; // Clear previous inputs
var inputs = figureInputs[currentFigureType];
for (var i = 0; i < inputs.length; i++) {
var inputData = inputs[i];
var div = document.createElement("div");
div.className = "input-group";
var label = document.createElement("label");
label.setAttribute("for", inputData.id);
label.textContent = inputData.label;
div.appendChild(label);
var input = document.createElement("input");
input.setAttribute("type", inputData.type);
input.setAttribute("id", inputData.id);
input.setAttribute("name", inputData.id);
input.setAttribute("placeholder", " "); // Placeholder for styling
input.setAttribute("oninput", "validateInput('" + inputData.id + "')");
input.setAttribute("data-label", inputData.label); // Store for validation message
div.appendChild(input);
var helper = document.createElement("span");
helper.className = "helper-text";
helper.textContent = inputData.helper;
div.appendChild(helper);
var errorSpan = document.createElement("span");
errorSpan.setAttribute("id", inputData.id + "Error");
errorSpan.className = "error-message";
div.appendChild(errorSpan);
inputsContainer.appendChild(div);
}
updateFormulaDisplay();
clearResults();
}
function updateFormulaDisplay() {
var formulaInfo = figureFormulas[currentFigureType];
document.getElementById("formulaDisplay").innerHTML = "" + formulaInfo.formula + "" + formulaInfo.explanation;
}
function validateInput(id) {
var input = document.getElementById(id);
var errorSpan = document.getElementById(id + "Error");
var value = input.value.trim();
var label = input.getAttribute("data-label");
if (value === "") {
errorSpan.textContent = "";
input.style.borderColor = "#ccc";
return false;
}
var numberValue = parseFloat(value);
if (isNaN(numberValue)) {
errorSpan.textContent = "Please enter a valid number.";
input.style.borderColor = "#dc3545";
return false;
}
if (numberValue <= 0) {
errorSpan.textContent = label + " must be a positive number.";
input.style.borderColor = "#dc3545";
return false;
}
errorSpan.textContent = "";
input.style.borderColor = "#28a745"; // Success color border
return true;
}
function validateAllInputs() {
var inputs = figureInputs[currentFigureType];
var allValid = true;
for (var i = 0; i < inputs.length; i++) {
if (!validateInput(inputs[i].id)) {
allValid = false;
}
}
return allValid;
}
function calculateArea() {
if (!validateAllInputs()) {
return;
}
var area = 0;
var intermediateValues = [];
var inputs = figureInputs[currentFigureType];
var inputValues = {};
for (var i = 0; i < inputs.length; i++) {
var input = document.getElementById(inputs[i].id);
inputValues[inputs[i].id] = parseFloat(input.value);
}
var pi = Math.PI;
switch (currentFigureType) {
case "square":
var side = inputValues.side;
area = side * side;
intermediateValues.push({ label: "Side", value: side + " units" });
intermediateValues.push({ label: "Side Squared", value: area.toFixed(2) + " sq units" });
break;
case "rectangle":
var length = inputValues.length;
var width = inputValues.width;
area = length * width;
intermediateValues.push({ label: "Length", value: length + " units" });
intermediateValues.push({ label: "Width", value: width + " units" });
intermediateValues.push({ label: "Length x Width", value: area.toFixed(2) + " sq units" });
break;
case "triangle":
var base = inputValues.base;
var height = inputValues.height;
area = 0.5 * base * height;
intermediateValues.push({ label: "Base", value: base + " units" });
intermediateValues.push({ label: "Height", value: height + " units" });
intermediateValues.push({ label: "0.5 x Base x Height", value: area.toFixed(2) + " sq units" });
break;
case "circle":
var radius = inputValues.radius;
area = pi * radius * radius;
intermediateValues.push({ label: "Radius", value: radius + " units" });
intermediateValues.push({ label: "Radius Squared", value: (radius * radius).toFixed(2) + " sq units" });
intermediateValues.push({ label: "π * Radius²", value: area.toFixed(2) + " sq units" });
break;
case "trapezoid":
var base1 = inputValues.base1;
var base2 = inputValues.base2;
var height = inputValues.height;
area = 0.5 * (base1 + base2) * height;
intermediateValues.push({ label: "Base 1", value: base1 + " units" });
intermediateValues.push({ label: "Base 2", value: base2 + " units" });
intermediateValues.push({ label: "Sum of Bases", value: (base1 + base2).toFixed(2) + " units" });
intermediateValues.push({ label: "0.5 * (B1+B2) * H", value: area.toFixed(2) + " sq units" });
break;
case "parallelogram":
var base = inputValues.base;
var height = inputValues.height;
area = base * height;
intermediateValues.push({ label: "Base", value: base + " units" });
intermediateValues.push({ label: "Height", value: height + " units" });
intermediateValues.push({ label: "Base x Height", value: area.toFixed(2) + " sq units" });
break;
case "ellipse":
var semiMajorAxis = inputValues.semiMajorAxis;
var semiMinorAxis = inputValues.semiMinorAxis;
area = pi * semiMajorAxis * semiMinorAxis;
intermediateValues.push({ label: "Semi-major Axis (a)", value: semiMajorAxis + " units" });
intermediateValues.push({ label: "Semi-minor Axis (b)", value: semiMinorAxis + " units" });
intermediateValues.push({ label: "π * a * b", value: area.toFixed(2) + " sq units" });
break;
}
document.getElementById("mainResultValue").textContent = area.toFixed(2);
var list = document.getElementById("intermediateResultsList");
list.innerHTML = "";
for (var j = 0; j < intermediateValues.length; j++) {
var li = document.createElement("li");
li.innerHTML = '' + intermediateValues[j].label + ':' + intermediateValues[j].value + '';
list.appendChild(li);
}
updateChart(area, intermediateValues); // Update chart
}
function resetCalculator() {
document.getElementById("figureType").value = "square";
updateInputs();
clearResults();
var inputsContainer = document.getElementById("inputsContainer");
var inputElements = inputsContainer.querySelectorAll("input");
for (var i = 0; i < inputElements.length; i++) {
inputElements[i].value = "";
document.getElementById(inputElements[i].id + "Error").textContent = "";
inputElements[i].style.borderColor = "#ccc";
}
}
function clearResults() {
document.getElementById("mainResultValue").textContent = "–";
document.getElementById("intermediateResultsList").innerHTML = "
No intermediate values yet.
";
var ctx = document.getElementById('areaChart').getContext('2d');
ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height); // Clear chart canvas
var chartContainer = document.getElementById('chartContainer');
if (chartContainer) {
chartContainer.style.display = 'none'; // Hide chart if cleared
}
}
function copyResults() {
var mainResult = document.getElementById("mainResultValue").textContent;
var resultUnit = "Square Units";
var formula = document.getElementById("formulaDisplay").textContent;
var intermediateList = document.getElementById("intermediateResultsList").querySelectorAll("li");
var intermediateText = "";
intermediateList.forEach(function(item) {
intermediateText += "- " + item.textContent.replace(":", ": ") + "\n";
});
if (mainResult === "–") {
alert("No results to copy yet.");
return;
}
var textToCopy = "Area Calculation Results:\n\n";
textToCopy += "Figure Type: " + document.getElementById("figureType").options[document.getElementById("figureType").selectedIndex].text + "\n";
textToCopy += "Calculated Area: " + mainResult + " " + resultUnit + "\n\n";
textToCopy += "Formula Used:\n" + formula + "\n\n";
textToCopy += "Intermediate Values:\n" + intermediateText;
navigator.clipboard.writeText(textToCopy).then(function() {
// Show a temporary success message
var originalButtonText = event.target.textContent;
event.target.textContent = "Copied!";
setTimeout(function() {
event.target.textContent = originalButtonText;
}, 2000);
}).catch(function(err) {
console.error('Could not copy text: ', err);
alert("Failed to copy results. Please copy manually.");
});
}
// Charting Logic
function updateChart(mainArea, intermediateValues) {
var ctx = document.getElementById('areaChart').getContext('2d');
var chartContainer = document.getElementById('chartContainer');
// Clear previous chart instance if it exists
if (window.myAreaChart) {
window.myAreaChart.destroy();
}
chartContainer.style.display = 'block'; // Make chart visible
var labels = [];
var dataValues = [];
var dataColors = ['rgba(0, 74, 153, 0.6)', 'rgba(40, 167, 69, 0.6)', 'rgba(255, 193, 7, 0.6)', 'rgba(108, 117, 125, 0.6)'];
var borderColors = ['rgba(0, 74, 153, 1)', 'rgba(40, 167, 69, 1)', 'rgba(255, 193, 7, 1)', 'rgba(108, 117, 125, 1)'];
// Primary result always first
labels.push("Calculated Area");
dataValues.push(mainArea);
// Add intermediate values if they are relevant parts of the area calculation
// This is a simplified approach; more complex logic might be needed for specific shapes
for (var i = 0; i < intermediateValues.length; i++) {
var value = parseFloat(intermediateValues[i].value);
if (!isNaN(value) && intermediateValues[i].label.includes("x") || intermediateValues[i].label.includes("²") || intermediateValues[i].label.includes("π")) {
labels.push(intermediateValues[i].label);
dataValues.push(value);
} else if (intermediateValues[i].label === "Radius" || intermediateValues[i].label === "Side" || intermediateValues[i].label === "Base") {
// Optionally add base dimensions if relevant to visualizing components
// labels.push(intermediateValues[i].label);
// dataValues.push(value);
}
}
// Ensure we have at least two data series for comparison if possible
if (dataValues.length < 2 && currentFigureType === "circle") {
var radius = parseFloat(document.getElementById("radius").value);
if (!isNaN(radius)) {
labels.push("Radius Squared");
dataValues.push(radius * radius);
}
} else if (dataValues.length maxSeries) {
// Keep the main result and take a few others, or simplify
labels = labels.slice(0, 1).concat(labels.slice(labels.length – (maxSeries – 1)));
dataValues = dataValues.slice(0, 1).concat(dataValues.slice(dataValues.length – (maxSeries – 1)));
}
window.myAreaChart = new Chart(ctx, {
type: 'bar', // Changed to bar for better visualization of components
data: {
labels: labels,
datasets: [{
label: 'Area Components (sq units)',
data: dataValues,
backgroundColor: dataColors.slice(0, dataValues.length), // Use available colors
borderColor: borderColors.slice(0, dataValues.length),
borderWidth: 1
}]
},
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
y: {
beginAtZero: true,
title: {
display: true,
text: 'Area (sq units)'
}
},
x: {
title: {
display: true,
text: 'Components'
}
}
},
plugins: {
title: {
display: true,
text: 'Breakdown of Area Calculation'
},
legend: {
display: false // Hide legend if labels are descriptive enough
}
}
}
});
}
// Initial setup
document.addEventListener("DOMContentLoaded", function() {
updateInputs();
// Add a placeholder for the chart canvas
var chartDiv = document.createElement('div');
chartDiv.id = 'chartContainer';
chartDiv.className = 'chart-container';
chartDiv.style.display = 'none'; // Initially hidden
var chartTitle = document.createElement('h4');
chartTitle.textContent = 'Area Calculation Breakdown';
chartDiv.appendChild(chartTitle);
var canvas = document.createElement('canvas');
canvas.id = 'areaChart';
chartDiv.appendChild(canvas);
document.querySelector('.calculator-section').appendChild(chartDiv);
});