Area of Quadrilateral Calculator
Calculate the area of any quadrilateral including rectangles, squares, parallelograms, rhombuses, trapezoids, and irregular quadrilaterals
Calculate Quadrilateral Area
Calculation Results
Example Calculation
Rectangle Example
Given: Length = 8 m, Width = 5 m
Formula: Area = length × width
Calculation: Area = 8 × 5 = 40 m²
Irregular Quadrilateral Example
Given: Diagonals = 12 m and 8 m, Angle = 90°
Formula: Area = ½ × e × f × sin(α)
Calculation: Area = ½ × 12 × 8 × sin(90°) = 48 m²
Quadrilateral Types
Rectangle
Opposite sides equal, all angles 90°
Square
All sides equal, all angles 90°
Parallelogram
Opposite sides parallel and equal
Rhombus
All sides equal, diagonals perpendicular
Trapezoid
One pair of parallel sides
Kite
Two pairs of adjacent equal sides
Area Formulas
Rectangle:
A = l × w
Square:
A = s²
Parallelogram:
A = b × h
Rhombus/Kite:
A = ½ × d₁ × d₂
Trapezoid:
A = ½ × h × (a + b)
From Diagonals:
A = ½ × e × f × sin(α)
Understanding Quadrilateral Area Calculations
What is a Quadrilateral?
A quadrilateral is a polygon with four sides and four vertices. The sum of all interior angles in any quadrilateral is always 360°. Quadrilaterals can be regular (with equal sides and angles) or irregular (with different sides and angles).
Common Types
- •Rectangle: Opposite sides are equal and parallel, all angles are 90°
- •Square: All sides are equal, all angles are 90°
- •Parallelogram: Opposite sides are parallel and equal
- •Rhombus: All sides are equal, diagonals bisect at right angles
Calculation Methods
The area calculation method depends on the known parameters of the quadrilateral:
For Regular Quadrilaterals
Use specific formulas based on the shape (rectangle, square, etc.)
For Irregular Quadrilaterals
Use Bretschneider's formula, diagonal method, or coordinate geometry
Shoelace Formula
When coordinates of all vertices are known
Important Formulas
Bretschneider's Formula
A = √[(s-a)(s-b)(s-c)(s-d) - abcd·cos²((α+γ)/2)]
Where s is the semi-perimeter and α, γ are opposite angles
Diagonal Method
A = ½ × e × f × sin(θ)
Where e and f are diagonals, θ is the angle between them