Geometry Tool
Rectangle Calculator
Calculate the area, perimeter, and diagonal length of a rectangle given its length and width. Easy to use with real-world examples and step-by-step calculations.
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Interactive Rectangle Calculator Workspace
Outputs
Area108.00
Perimeter42.00
Diagonal15.00
Worked Equations
1. Area: Length × Width = 12 × 9 = 108.00
2. Perimeter: 2 × (Length + Width) = 2 × (12 + 9) = 42.00
3. Diagonal: √(Length² + Width²) = √(12² + 9²) = √(144 + 81) = 15.00
Mathematical Formula & Variables
Equation Model
Area = l × w, Perimeter = 2 × (l + w), Diagonal = √(l² + w²)Calculates the primary properties of a 4-sided right-angled quadrilateral (rectangle) using length and width dimensions.
Variable Definitions
| Symbol | Description |
|---|---|
| l (Length) | The longer side dimension of the rectangle. |
| w (Width) | The shorter side dimension of the rectangle. |
| A (Area) | The enclosed flat surface space inside the rectangle. |
| P (Perimeter) | The sum of all four side lengths. |
| d (Diagonal) | The straight-line distance between opposite corners. |
How to Use the Rectangle Calculator
- Enter the Length of the rectangle in the input field.
- Enter the Width of the rectangle in the adjacent field.
- Review the calculated Area, Perimeter, and Diagonal length updated in real-time.
- Inspect the step-by-step worked calculations to understand how the diagonals relate to the Pythagorean Theorem.
Practical Example Calculation
Scenario Context: You want to buy a rug for a room that measures 12 feet long and 9 feet wide.
Step 1: Identify knowns: Length (l) = 12 ft, Width (w) = 9 ft.
Step 2: Calculate Area (A): A = l × w = 12 × 9 = 108 square feet.
Step 3: Calculate Perimeter (P): P = 2 × (l + w) = 2 × (12 + 9) = 2 × 21 = 42 feet.
Step 4: Calculate Diagonal (d): d = √(l² + w²) = √(12² + 9²) = √(144 + 81) = √225 = 15 feet.
The rug area is 108 sq ft, perimeter is 42 ft, and diagonal corner-to-corner length is 15 ft.
Frequently Asked Questions
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