Area of Quadrilateral Calculator

Result:

Method: Shoelace Formula
Area = 12.0000 square units

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How It Works

1

Choose Method

Select calculation type

2

Enter Data

Input coordinates or diagonals

Area calculated

Common Examples

Rectangle: (0,0), (4,0), (4,3), (0,3)
Area = 12 square units
Square: d₁ = d₂ = 5√2, θ = 90°
Area = 25 square units
Formulas
Shoelace: A = ½|∑(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)|
Diagonals: A = ½ × d₁ × d₂ × sin(θ)

Area of Quadrilateral Calculator

What

Calculate the area of any quadrilateral using coordinates or diagonal measurements.

🎯

Why

Essential for geometry, land surveying, architecture, and engineering projects.

Applications

Construction planning, area measurement, geometric analysis, and educational purposes.

📊 Calculation Examples

Rectangle
Points:(0,0), (4,0), (4,3), (0,3)
Area:12 sq units
Shoelace Formula
Square (Diagonals)
d₁, d₂:5√2, 5√2
Angle:90°
Area:25 sq units
Diagonal Formula
Rhombus
d₁, d₂:8, 6
Angle:90°
Area:24 sq units
Diagonal Formula

Frequently Asked Questions

1

What is a quadrilateral?

A quadrilateral is a polygon with four sides and four vertices. Examples include squares, rectangles, rhombuses, parallelograms, and trapezoids.

2

What is the Shoelace formula?

The Shoelace formula calculates the area of a polygon using its vertex coordinates: A = ½|∑(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)|. It works for any simple polygon.

3

How do I use the diagonal method?

Enter the lengths of both diagonals and the angle between them. The formula is: Area = ½ × d₁ × d₂ × sin(θ).

4

What order should I enter coordinates?

Enter coordinates in order around the quadrilateral (clockwise or counterclockwise). The Shoelace formula automatically handles the calculation.

5

Can I calculate irregular quadrilaterals?

Yes! Both methods work for any quadrilateral shape, including irregular ones. The coordinate method is especially useful for complex shapes.

6

What units does the calculator use?

The calculator works with any consistent units. If you input lengths in meters, the area will be in square meters. Always use the same units for all measurements.

7

Is this calculator accurate for all quadrilaterals?

Yes, both the Shoelace formula and diagonal method are mathematically precise for all types of quadrilaterals, providing accurate area calculations.

Area Formulas

A = ½|∑(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)|
Shoelace formula
A = ½ × d₁ × d₂ × sin(θ)
Diagonal method

Quick Examples

Rectangle 4×3
Area = 12
Square d=5√2
Area = 25

💡 Tips

• Use coordinates for irregular shapes
• Diagonal method works for all quadrilaterals
• Enter points in order around perimeter
• Keep units consistent throughout