Quadrilateral Calculator
Calculate area and perimeter of any quadrilateral. Automatically identifies the quadrilateral type.
Quadrilateral Dimensions
Diagonals (optional for better accuracy):
Results:
Type: Unknown
Perimeter: 0.00 units
Area: 0.00 square units
Step-by-Step Solution:
About Quadrilaterals
What is a Quadrilateral?
A quadrilateral is any polygon with four sides and four vertices. The sum of interior angles always equals 360°. Common types include squares, rectangles, parallelograms, trapezoids, rhombuses, and kites.
Types of Quadrilaterals
- Square: All sides equal, all angles 90°
- Rectangle: Opposite sides equal, all angles 90°
- Parallelogram: Opposite sides parallel and equal
- Rhombus: All sides equal, opposite angles equal
- Trapezoid: One pair of parallel sides
- Kite: Two pairs of consecutive equal sides
Key Properties
- Has four sides and four vertices
- Sum of interior angles = 360°
- Has two diagonals
- Can be convex or concave
- Perimeter = sum of all four sides
Area Formulas
Bretschneider's Formula: General quadrilateral area
Brahmagupta's Formula: For cyclic quadrilaterals
Diagonal Method: A = ½ × d₁ × d₂ × sin(θ)
Frequently Asked Questions
What is the sum of angles in a quadrilateral?
The sum of all interior angles in any quadrilateral is always 360°. This applies to all types of quadrilaterals, whether regular or irregular.
How many diagonals does a quadrilateral have?
Every quadrilateral has exactly 2 diagonals. These are line segments connecting non-adjacent vertices.
Can any four lengths form a quadrilateral?
No. The sum of any three sides must be greater than the fourth side. This is similar to the triangle inequality but applied to quadrilaterals.
What is a cyclic quadrilateral?
A cyclic quadrilateral is one where all four vertices lie on a single circle. Opposite angles in a cyclic quadrilateral are supplementary (sum to 180°).
How do you calculate the area?
For general quadrilaterals, you need additional information beyond just the sides (like diagonals or angles). Special quadrilaterals have simpler area formulas based on their properties.
What's a convex vs concave quadrilateral?
A convex quadrilateral has all interior angles less than 180° and both diagonals lie inside. A concave quadrilateral has one interior angle greater than 180°.