Rectangle formulas with Calculation Examples

A rectangle is a quadrilateral with four right angles. Commonly  used formulas to calculate various properties of a rectangle.

• Rectangle Exercises and problems;
• Rectangle Quiz and Trivia questions;
   

Rectangle formulas 

1. Area of a Rectangle (A): The area of a rectangle can be calculated by multiplying its length (L) by its width (W). Formula: A = L × W

2. Perimeter of a Rectangle (P): The perimeter of a rectangle is the sum of all its sides. Formula: P = 2(L + W) or P = 2L + 2W

   
   
   

3. Diagonal of a Rectangle (D): The diagonal of a rectangle can be calculated using the Pythagorean Theorem, as the diagonal creates a right triangle with the length and width as its legs. Formula: D = √(L² + W²)

4. Length of a Rectangle (L): You can find the length of a rectangle if you know its area and width. Formula: L = A / W

5. Width of a Rectangle (W): You can find the width of a rectangle if you know its area and length. Formula: W = A / L

6. Ratio of Length to Width (L:W): This is the ratio of the length to the width of a rectangle. Formula: L:W = L / W

 

These formulas are fundamental for calculating various properties of rectangles, including their area, perimeter, and diagonal, as well as for finding one dimension when you know the other.

 

Examples to calculate properties of rectangles

Example 1: Find the area and perimeter of a rectangle with a length of 8 units and a width of 5 units.

1. Area (A): A = L × W A = 8 units × 5 units A = 40 square units

2. Perimeter (P): P = 2(L + W) P = 2(8 units + 5 units) P = 2(13 units) P = 26 units

So, the area of the rectangle is 40 square units, and its perimeter is 26 units.

Example 2: Find the diagonal of a rectangle with a length of 12 units and a width of 9 units.

3. Diagonal (D): D = √(L² + W²) D = √((12 units)² + (9 units)²) D = √(144 + 81) D = √225 D = 15 units

The diagonal of the rectangle is 15 units.

Example 3: Given the area of a rectangle is 48 square meters and its width is 6 meters, find its length.

4. Length (L): L = A / W L = 48 square meters / 6 meters L = 8 meters

So, the length of the rectangle is 8 meters.

Example 4: Given the perimeter of a rectangle is 30 inches, and its width is 4 inches, find its length.

5. Length (L): P = 2(L + W) 30 inches = 2(L + 4 inches) 15 inches = L + 4 inches

Subtract 4 inches from both sides: 15 inches - 4 inches = L 11 inches = L

The length of the rectangle is 11 inches.