Use this calculator to determine the area of a shaded region, specifically for a scenario where a circle is removed from the center of a rectangle. This is a common type of problem in geometry where you find the area of a larger shape and subtract the area of a smaller, unshaded shape within it.
function calculateShadedArea() {
var rectLengthInput = document.getElementById("rectLength").value;
var rectWidthInput = document.getElementById("rectWidth").value;
var circleRadiusInput = document.getElementById("circleRadius").value;
var rectLength = parseFloat(rectLengthInput);
var rectWidth = parseFloat(rectWidthInput);
var circleRadius = parseFloat(circleRadiusInput);
var resultDiv = document.getElementById("shadedAreaResult");
if (isNaN(rectLength) || isNaN(rectWidth) || isNaN(circleRadius) || rectLength <= 0 || rectWidth <= 0 || circleRadius < 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all dimensions.";
return;
}
var areaRectangle = rectLength * rectWidth;
var areaCircle = Math.PI * circleRadius * circleRadius;
var shadedArea = areaRectangle – areaCircle;
if (shadedArea < 0) {
resultDiv.innerHTML = "The circle's area (" + areaCircle.toFixed(2) + " sq units) is larger than the rectangle's area (" + areaRectangle.toFixed(2) + " sq units). The calculated shaded area would be " + shadedArea.toFixed(2) + " square units. Please ensure the circle fits within the rectangle for a positive shaded area.";
} else {
resultDiv.innerHTML = "The area of the rectangle is: " + areaRectangle.toFixed(2) + " square units.";
resultDiv.innerHTML += "The area of the circle is: " + areaCircle.toFixed(2) + " square units.";
resultDiv.innerHTML += "The Shaded Area is:
.";
}
}
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padding: 12px 20px;
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width: 100%;
transition: background-color 0.3s ease;
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.calculator-inputs button:hover {
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.calculator-result {
background-color: #e9ecef;
padding: 15px;
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font-size: 1.2em;
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Understanding Shaded Regions in Geometry
In geometry, a "shaded region" refers to a specific area within a larger figure that is highlighted or distinguished from the rest. Calculating the area of a shaded region is a common problem that often involves combining or subtracting the areas of basic geometric shapes like rectangles, circles, triangles, or squares.
Common Scenarios for Shaded Regions
There are several typical ways a shaded region might be presented:
- Subtraction of Areas: A smaller shape is removed or cut out from a larger shape. The shaded region is the remaining area. This is the scenario our calculator addresses.
- Overlapping Areas: Two or more shapes overlap, and the shaded region is the area where they intersect.
- Composite Shapes: The shaded region itself is made up of several simpler shapes joined together.
How Our Calculator Works (Rectangle with a Circular Cutout)
This calculator is designed for a specific, yet very common, type of shaded region problem: finding the area of a rectangle after a circular section has been removed from its interior. Imagine a rectangular piece of wood with a circular hole drilled through it. The shaded region would be the remaining wood.
The calculation follows a straightforward principle:
- Calculate the Area of the Larger Shape (Rectangle): The area of a rectangle is found by multiplying its length by its width.
- Calculate the Area of the Smaller Shape (Circle): The area of a circle is found using the formula πr², where π (Pi) is approximately 3.14159, and 'r' is the radius of the circle.
- Subtract the Smaller Area from the Larger Area: The area of the shaded region is simply the area of the rectangle minus the area of the circle.
Formulas Used:
- Area of Rectangle = Length × Width
- Area of Circle = π × Radius²
- Area of Shaded Region = Area of Rectangle – Area of Circle
Example Calculation:
Let's say you have a rectangular sheet with the following dimensions:
- Rectangle Length = 10 units
- Rectangle Width = 8 units
- Circle Radius = 3 units
Using the formulas:
- Area of Rectangle: 10 × 8 = 80 square units
- Area of Circle: π × (3)² = π × 9 ≈ 28.27 square units
- Area of Shaded Region: 80 – 28.27 = 51.73 square units
This calculator automates these steps, providing you with the shaded area quickly and accurately.