Square Foot Calculator Quadrilateral
Calculate the square footage of any quadrilateral. Enter the two diagonals and the angle between them to get the area.
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.