Composite Figure Calculator

Composite Figure Area & Perimeter Calculator

This calculator determines the area and perimeter of a composite figure made from a rectangle with a semicircle attached to one of its width sides.

function calculateCompositeFigure() { var rectangleLengthInput = document.getElementById('rectangleLength').value; var rectangleWidthInput = document.getElementById('rectangleWidth').value; var errorMessagesDiv = document.getElementById('errorMessages'); errorMessagesDiv.innerHTML = "; // Clear previous errors var rectangleLength = parseFloat(rectangleLengthInput); var rectangleWidth = parseFloat(rectangleWidthInput); if (isNaN(rectangleLength) || isNaN(rectangleWidth) || rectangleLength <= 0 || rectangleWidth <= 0) { errorMessagesDiv.innerHTML = 'Please enter valid positive numbers for all dimensions.'; document.getElementById('totalArea').textContent = '0'; document.getElementById('totalPerimeter').textContent = '0'; return; } // Calculate Area var rectArea = rectangleLength * rectangleWidth; var semicircleRadius = rectangleWidth / 2; var semicircleArea = 0.5 * Math.PI * Math.pow(semicircleRadius, 2); var totalArea = rectArea + semicircleArea; // Calculate Perimeter // The perimeter consists of two lengths of the rectangle, one width of the rectangle, // and the arc length of the semicircle. The side where the semicircle is attached is internal. var rectPerimeterPart = (2 * rectangleLength) + rectangleWidth; var semicircleCircumference = Math.PI * semicircleRadius; var totalPerimeter = rectPerimeterPart + semicircleCircumference; document.getElementById('totalArea').textContent = totalArea.toFixed(2); document.getElementById('totalPerimeter').textContent = totalPerimeter.toFixed(2); }

Understanding Composite Figures

A composite figure, also known as a compound shape, is a shape that is made up of two or more basic geometric shapes. These basic shapes can include rectangles, triangles, circles, semicircles, trapezoids, and more. Calculating the area and perimeter of such figures requires breaking them down into their simpler components, calculating the properties of each component, and then combining them appropriately.

The Specific Composite Figure This Calculator Handles

This calculator is designed for a common composite figure: a rectangle with a semicircle attached to one of its width sides. Imagine a building with a rounded roof, or a window with an arched top. The semicircle's diameter is equal to the rectangle's width, meaning it perfectly caps one side of the rectangle.

For example, if you have a rectangle that is 10 units long and 4 units wide, and a semicircle is attached to one of the 4-unit sides, the semicircle will have a diameter of 4 units (and thus a radius of 2 units).

Formulas Used in Calculation

To find the total area and perimeter of this specific composite figure, we use the following formulas:

Area Calculation:

• Area of Rectangle: Length × Width
• Area of Semicircle: 0.5 × π × (Radius)²
• Total Area: Area of Rectangle + Area of Semicircle

Where the Semicircle Radius is Width of Rectangle / 2.

Perimeter Calculation:

The perimeter is the total distance around the outer boundary of the shape. For our composite figure, it includes:

• Two sides of the rectangle (the two lengths).
• One side of the rectangle (the width that is not attached to the semicircle).
• The arc length of the semicircle.

The side of the rectangle where the semicircle is attached becomes an internal boundary and is therefore not part of the overall perimeter.

• Perimeter of Semicircle Arc: π × Radius (which is half the circumference of a full circle)
• Total Perimeter: (2 × Rectangle Length) + Rectangle Width (unattached side) + Perimeter of Semicircle Arc

Example Calculation

Let's use the default values in the calculator:

• Rectangle Length: 10 units
• Rectangle Width: 4 units

Area:

1. Rectangle Area: 10 units × 4 units = 40 square units
2. Semicircle Radius: 4 units / 2 = 2 units
3. Semicircle Area: 0.5 × π × (2 units)² = 0.5 × 3.14159 × 4 = 6.28 square units (approximately)
4. Total Area: 40 + 6.28 = 46.28 square units

Perimeter:

1. Rectangle Perimeter Parts: (2 × 10 units) + 4 units = 20 + 4 = 24 units
2. Semicircle Arc Length: π × 2 units = 6.28 units (approximately)
3. Total Perimeter: 24 + 6.28 = 30.28 units

Using this calculator, you can quickly find these values for various dimensions, making it easier to work with composite figures in geometry, engineering, or design.