Square Foot Calculator Quadrilateral
Calculate square footage of any quadrilateral from 2 diagonals and angle. Instant results in sq ft, m², and acres. Free online tool.
Quadrilateral Calculator
Enter the two diagonals and the angle between them.
Diagonals connect opposite corners.
θ is the angle where they cross.
How to Calculate Square Footage of a Quadrilateral
A quadrilateral is any 4-sided polygon. When the shape is not a standard rectangle, trapezoid, or parallelogram, the diagonal method provides the most reliable area calculation.
Quadrilateral Area Formula
Where d₁ and d₂ are the two diagonals and θ is the angle where they intersect. For perpendicular diagonals (90°), sin(90°) = 1, simplifying to ½ × d₁ × d₂.
Step-by-Step Instructions
- Draw or identify the two diagonals — lines connecting opposite corners.
- Measure each diagonal in feet.
- Measure the angle where the diagonals cross (in degrees).
- Apply the formula: ½ × d₁ × d₂ × sin(θ).
Example Calculation
A 4-sided yard section has diagonals of 15 ft and 12 ft crossing at 90°.
½ × 15 × 12 × sin(90°) = ½ × 15 × 12 × 1 = 90 square feet (8.36 sq m)
Common Uses
- Irregularly shaped property lots
- Non-rectangular room sections
- Diamond or kite-shaped areas
- Oddly angled garden plots
Frequently Asked Questions
How do I calculate the area of an irregular quadrilateral? +
Use the diagonal method: Area = ½ × d₁ × d₂ × sin(θ), where d₁ and d₂ are the two diagonals and θ is the angle between them.
What angle should I use for perpendicular diagonals? +
If the diagonals cross at a right angle (90°), use 90. Since sin(90°) = 1, the formula simplifies to Area = ½ × d₁ × d₂.
What shapes are quadrilaterals? +
Rectangles, squares, parallelograms, rhombuses, trapezoids, and kites are all quadrilaterals (4-sided polygons).
How do I measure the diagonals of a quadrilateral? +
Draw or imagine lines connecting opposite corners. Measure each diagonal length and the angle where they cross.