Rectangle Area Calculator
Calculate the area, perimeter, and diagonal of a rectangle by entering its length and width.
Notes:
- Area is calculated as length × width (A = l × w)
- Perimeter is calculated as 2 × (length + width) (P = 2l + 2w)
- Diagonal is calculated using the Pythagorean theorem: d = √(l² + w²)
- Area is expressed in square units (e.g., cm², m², in²)
- Perimeter is expressed in linear units (e.g., cm, m, in)
- A square is a special type of rectangle where length equals width
Understanding Rectangle Calculations
A rectangle is a four-sided shape with opposite sides equal in length and all angles equal to 90 degrees. It is one of the most common shapes in everyday life, appearing in buildings, furniture, screens, paper, and countless other objects.
Rectangle Formulas
Area
where l is the length and w is the width
Perimeter
the distance around the rectangle
Diagonal
using the Pythagorean theorem
Rectangle Area
The area of a rectangle is the space enclosed within its boundaries. It is calculated by multiplying the length by the width: A = l × w.
For example, if a rectangle has a length of 6 cm and a width of 4 cm, its area would be:
A = 6 × 4 = 24 cm²
The area of a rectangle represents how many unit squares (squares with side length 1 unit) can fit inside it. In the example above, 24 squares of size 1 cm × 1 cm could fit inside the rectangle.
Rectangle Perimeter
The perimeter of a rectangle is the total distance around its outside. It is calculated by adding all four sides: P = l + w + l + w = 2l + 2w = 2(l + w).
For example, if a rectangle has a length of 6 cm and a width of 4 cm, its perimeter would be:
P = 2(6) + 2(4) = 12 + 8 = 20 cm
The perimeter is important for determining the amount of material needed to enclose an area, such as fencing for a yard or framing for a picture.
Rectangle Diagonal
The diagonal of a rectangle is the straight line connecting opposite corners. It is calculated using the Pythagorean theorem: d = √(l² + w²).
For example, if a rectangle has a length of 6 cm and a width of 4 cm, its diagonal would be:
d = √(6² + 4²) = √(36 + 16) = √52 ≈ 7.21 cm
The diagonal of a rectangle divides it into two congruent right triangles. The diagonal is also the longest straight line that can be drawn within a rectangle.
Properties of Rectangle Diagonals
- The two diagonals of a rectangle are equal in length
- The diagonals bisect each other (they divide each other in half at their intersection)
- The diagonals of a rectangle form congruent triangles
Special Case: Squares
A square is a special type of rectangle where all sides are equal in length (l = w).
Square Area
where s is the side length
Square Perimeter
where s is the side length
Square Diagonal
where s is the side length
For example, if a square has sides of length 5 cm, then:
- Area = 5² = 25 cm²
- Perimeter = 4 × 5 = 20 cm
- Diagonal = 5√2 ≈ 7.07 cm
Practical Applications of Rectangle Calculations
Construction & Architecture
- Calculating flooring or roofing materials
- Determining wall surface for paint
- Planning room layouts
- Designing windows and doors
- Measuring land for building projects
Everyday Life
- Calculating material for tablecloths
- Measuring fabric for curtains
- Determining carpet or tile requirements
- Planning furniture placement
- Measuring TV or screen sizes (diagonal)
Manufacturing & Design
- Designing packaging
- Creating picture frames
- Planning material cuts for efficiency
- Calculating material costs
- Designing signs and displays