Rectangle Calculator

What is a Rectangle?

A rectangle is a four-sided polygon (quadrilateral) with opposite sides of equal length and all angles equal to 90 degrees.

Key Properties of Rectangles

• Opposite sides are equal in length
• All angles are right angles (90 degrees)
• Diagonals bisect each other
• Diagonals are equal in length

Formulas for Rectangles

Let \(l\) be the length and \(w\) be the width. Then:

1. Area: \(A = l \\times w\)
2. Perimeter: \(P = 2(l + w)\)
3. Diagonal: \(d = \sqrt{l^2 + w^2}\)

Step-by-Step Calculations

Let's calculate these properties for a rectangle with length \(l = 5\) units and width \(w = 3\) units:

1. Area: \[A = l \times w = 5 \times 3 = 15 \text{ square units}\]
2. Perimeter: \[P = 2(l + w) = 2(5 + 3) = 16 \text{ units}\]
3. Diagonal: \[d = \sqrt{l^2 + w^2} = \sqrt{5^2 + 3^2} \approx 5.83 \text{ units}\]

Visual Representation

This diagram illustrates the rectangle with the calculated dimensions and properties.