▱ Quadrilateral Calculator
Calculate area and perimeter of quadrilaterals
How to Use This Calculator
Choose Calculation Method
Select whether you know the four side lengths or the diagonals and angle between them.
Enter Values
Input the required measurements based on your selected method.
Click Calculate
Press the "Calculate Quadrilateral Properties" button to get area and/or perimeter.
Formulas
Method 1: Using Diagonals and Angle
Area = ½ × d₁ × d₂ × sin(θ)
Where d₁, d₂ are diagonals and θ is the angle between them
Method 2: Using Four Sides (Brahmagupta's Formula)
Area = √[(s-a)(s-b)(s-c)(s-d)]
Where s = (a+b+c+d)/2 (semi-perimeter) - for cyclic quadrilaterals
Perimeter
Perimeter = s₁ + s₂ + s₃ + s₄
About Quadrilateral Calculator
The Quadrilateral Calculator helps you find the area and perimeter of quadrilaterals (four-sided polygons). Quadrilaterals include squares, rectangles, parallelograms, trapezoids, and general four-sided shapes.
When to Use This Calculator
- Geometry: Calculate area and perimeter for quadrilateral problems
- Construction: Estimate materials needed for quadrilateral-shaped areas
- Land Surveying: Calculate area of four-sided land plots
- Education: Learn and practice quadrilateral mathematics
- Design: Calculate dimensions for quadrilateral designs
- Real Estate: Estimate property areas and boundaries
Why Use Our Calculator?
- ✅ Two Methods: Calculate using sides or diagonals
- ✅ Instant Results: Get area and perimeter immediately
- ✅ Flexible Input: Choose method based on available data
- ✅ Works with Any Units: Meters, feet, inches, or any unit
- ✅ 100% Accurate: Precise geometric calculations
- ✅ Completely Free: No registration required
Understanding Quadrilaterals
A quadrilateral is any four-sided polygon. Common types:
- Square: All sides equal, all angles 90°
- Rectangle: Opposite sides equal, all angles 90°
- Parallelogram: Opposite sides parallel and equal
- Trapezoid: One pair of parallel sides
- Rhombus: All sides equal, opposite angles equal
- General Quadrilateral: Any four-sided shape
Real-World Applications
Land Measurement: Many properties have quadrilateral shapes. Using diagonals and angle method is useful when you can measure diagonal lengths.
Construction: Calculate area for flooring, roofing, or fencing in quadrilateral-shaped areas. Perimeter helps estimate material lengths.
Design: Quadrilaterals are fundamental shapes in design and architecture. Calculate areas for layout planning.
Frequently Asked Questions
What is a quadrilateral?
A quadrilateral is any four-sided polygon. It has four vertices, four sides, and interior angles that sum to 360°.
How do I calculate quadrilateral area?
There are several methods: 1) Using diagonals and angle: Area = ½ × d₁ × d₂ × sin(θ). 2) Using sides (Brahmagupta's formula for cyclic quadrilaterals). 3) Special formulas for squares, rectangles, parallelograms, etc.
What is Brahmagupta's formula?
Brahmagupta's formula calculates the area of a cyclic quadrilateral (one that can be inscribed in a circle) using its four sides: Area = √[(s-a)(s-b)(s-c)(s-d)], where s is the semi-perimeter.
Can I use the diagonal method for any quadrilateral?
Yes, the diagonal method (Area = ½ × d₁ × d₂ × sin(θ)) works for any quadrilateral where you know the diagonal lengths and the angle between them.
What's the difference between a quadrilateral and a rectangle?
A rectangle is a specific type of quadrilateral with all angles equal to 90° and opposite sides equal. All rectangles are quadrilaterals, but not all quadrilaterals are rectangles.
How do I find perimeter of a quadrilateral?
Perimeter = sum of all four sides. Simply add the lengths of sides 1, 2, 3, and 4 together.
What is a cyclic quadrilateral?
A cyclic quadrilateral is one where all four vertices lie on a circle. For cyclic quadrilaterals, Brahmagupta's formula provides an exact area calculation using just the side lengths.