GEOMETRY2D GeometryMathematics Calculator
▱

Quadrilateral

Quadrilaterals have 4 sides and interior angles summing to 360°. Square, rectangle, rhombus, parallelogram, trapezoid, kite—each has a specific area formula. Choose the one matching your shape.

Concept Fundamentals
A=s², P=4s
Square
A=l×w, P=2(l+w)
Rectangle
A=½(a+c)h
Trapezoid
A=½d₁d₂
Kite

Did our AI summary help? Let us know.

Square and rectangle are special parallelograms with right angles. Rhombus has all sides equal; kite has two pairs of adjacent equal sides. Trapezoid has exactly one pair of parallel sides (bases).

Key quantities
A=s², P=4s
Square
Key relation
A=l×w, P=2(l+w)
Rectangle
Key relation
A=½(a+c)h
Trapezoid
Key relation
A=½d₁d₂
Kite
Key relation

Ready to run the numbers?

Why: Quadrilaterals are the most common shapes—tiles, rooms, land. Each type has unique properties: trapezoid has one pair parallel, kite has two pairs adjacent equal sides.

How: Square: A=s². Rectangle: A=l×w. Rhombus: A=s²sin(θ) or ½d₁d₂. Parallelogram: A=b×h. Trapezoid: A=½(a+c)h. Kite: A=½d₁d₂. Use the formula matching your shape.

Square and rectangle are special parallelograms with right angles.Rhombus has all sides equal; kite has two pairs of adjacent equal sides.
Sources:Wolfram MathWorld - QuadrilateralKhan Academy - Quadrilaterals

Run the calculator when you are ready.

Quadrilateral CalculatorSelect shape type and enter dimensions for area and perimeter
◼️
GEOMETRY2D Quadrilaterals

Quadrilateral — All Four-Sided Shapes

Square, rectangle, rhombus, parallelogram, trapezoid, kite, and general quadrilateral.

Square →Rectangle →Crescent →

📐 Real-World Examples — Click to Load

Calculation Settings

For educational and informational purposes only. Verify with a qualified professional.

🧮 Fascinating Math Facts

▱

Quadrilateral interior angles sum to 360°.

— Property

📐

Each quadrilateral type has a specific area formula.

— Formulas

📋 Key Takeaways

  • • Quadrilaterals have 4 sides and interior angles summing to 360°
  • • Square and rectangle are special parallelograms with right angles
  • • Rhombus has all sides equal; kite has two pairs of adjacent equal sides
  • • Trapezoid has exactly one pair of parallel sides
  • • Area formulas vary by type — use the one matching your shape

💡 Did You Know?

📐The word "quadrilateral" comes from Latin: quadri (four) + latus (side)Source: Etymology
🏛️Roman architects used trapezoidal shapes in amphitheater design for better acousticsSource: Architecture
🧮A square is the only regular quadrilateral — all sides and angles equalSource: Geometry
🎯Kites have perpendicular diagonals; one bisects the otherSource: Wolfram MathWorld
💻Computer graphics use quadrilaterals for texture mapping and 3D meshesSource: Tech
🔬Crystal structures often form rhombic or parallelogram unit cellsSource: Crystallography

📖 Formulas Explained

Square & Rectangle

Asquare=s2,Arect=l×wA_{\text{square}} = s^2, \quad A_{\text{rect}} = l \times w

Rhombus & Parallelogram

Arhombus=s2sin⁡θ,Apara=b×hA_{\text{rhombus}} = s^2 \sin\theta, \quad A_{\text{para}} = b \times h

Trapezoid & Kite

Atrap=(a+c)h2,Akite=d1×d22A_{\text{trap}} = \frac{(a+c)h}{2}, \quad A_{\text{kite}} = \frac{d_1 \times d_2}{2}

🎯 Expert Tips

Identify First

Check parallel sides and equal sides to classify your quadrilateral before choosing a formula.

Height is Perpendicular

For parallelogram and trapezoid, height is always perpendicular to the base.

Diagonals for Kite/Rhombus

Area = (d₁ × d₂)/2 when diagonals are known. Diagonals are perpendicular in both.

General Quad

For irregular quads, use Bretschneider formula or split into triangles if you have diagonals.

⚖️ Comparison Table

TypeArea FormulaMin Inputs
Squares²1
Rectanglel×w2
Rhombuss² sin θ2
Parallelogramb×h3
Trapezoid(a+c)h/23
Kited₁d₂/22

📊 Quick Facts

4
Sides
360°
Angle Sum
7
Types
2
Diagonals

❓ FAQ

What is a quadrilateral?

A four-sided polygon. Types include square, rectangle, rhombus, parallelogram, trapezoid, and kite.

How do I find the area of a rhombus?

Use A = s² sin(θ) with side and one angle, or A = (d₁×d₂)/2 with diagonals.

What is the difference between a rhombus and a kite?

Rhombus has all 4 sides equal. Kite has two pairs of adjacent equal sides.

Can a trapezoid have right angles?

Yes. A right trapezoid has two right angles adjacent to one of the parallel sides.

How do I calculate a general quadrilateral?

Use diagonals: A ≈ (d₁×d₂)/2, or split into two triangles and sum their areas.

What is the perimeter of a kite?

P = 2(a + b) where a and b are the lengths of the two pairs of equal sides.

Why does a square have the most area for a given perimeter?

Among rectangles with fixed perimeter, the square maximizes area (isoperimetric property).

How do I measure height in a parallelogram?

Height is the perpendicular distance from the base to the opposite side.

⚠️ Disclaimer: Results assume Euclidean geometry. Real-world measurements may vary. Verify for construction and engineering.

🚀 DIVING IN
🏊Let's explore the numbers!
AI

Related Calculators

Octagon Calculator

Octagon Calculator - Calculate area, perimeter, and other properties of an octagon with step-by-step solutions

Mathematics

Perimeter Calculator

Calculate the perimeter of various geometric shapes including squares, rectangles, triangles, circles, and regular polygons.

Mathematics

Regular Polygon Calculator

Calculate properties of any regular polygon including side length, area, perimeter, interior angles, and inscribed/circumscribed circles

Mathematics

Trapezoid Calculator

Calculate area, perimeter, and other properties of a trapezoid with step-by-step solutions.

Mathematics

Segment Addition Postulate Calculator

Segment Addition Postulate Calculator - Calculate and learn about segment addition postulate concepts

Mathematics

Spiral Length Calculator

Calculate the length of a spiral curve based on different spiral types and parameters. Supports Archimedean and logarithmic spirals with step-by-step...

Mathematics