Trapezoid Calculator
Calculate trapezoid properties including area, perimeter, and geometric measurements. Our geometry calculator supports isosceles, right, and general trapezoids with step-by-step analysis and multiple unit systems.
Last updated: December 15, 2024
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Trapezoid Properties
Area
50.00 cm²
Perimeter
30.77 cm
Median Length
10.00 cm
Diagonal (approx)
11.00 cm
Trapezoid Type:
Isosceles Trapezoid
Formula Used:
A = ½(b₁ + b₂)h, legs = √(h² + ((b₁-b₂)/2)²)
Analysis:
Isosceles trapezoid with equal legs = 5.39 units
Trapezoid Properties:
- • Has exactly one pair of parallel sides (bases)
- • Area = ½(b₁ + b₂) × height
- • Median connects midpoints of legs and equals (b₁ + b₂)/2
- • Isosceles trapezoids have equal legs and equal base angles
Quick Example Result
Isosceles trapezoid with bases 8 cm and 12 cm, height 5 cm:
Area
50.0 cm²
Perimeter
30.8 cm
Median
10.0 cm
Leg Length
5.39 cm
How This Calculator Works
Our trapezoid calculator applies fundamental geometric principles to analyze quadrilaterals with one pair of parallel sides. The calculations use coordinate geometry, trigonometry, and the Pythagorean theorem to determine all trapezoid properties.
Essential Trapezoid Formulas
A = ½(b₁ + b₂) × h (area formula)P = b₁ + b₂ + l₁ + l₂ (perimeter)m = (b₁ + b₂)/2 (median length)l = √(h² + ((b₁-b₂)/2)²) (isosceles legs)These formulas apply to different trapezoid types. The area formula is universal, while leg calculations depend on whether the trapezoid is isosceles, right, or scalene.
Shows parallel bases, height, legs, and median
Geometry Foundation
Trapezoid calculations are based on properties of parallel lines and right triangles. When perpendiculars are dropped from the shorter base to the longer base, they create right triangles that help determine leg lengths. Our calculator handles different trapezoid types with specialized formulas for each configuration.
- Exactly one pair of parallel sides distinguishes trapezoids from other quadrilaterals
- The median (midsegment) is always parallel to bases and equals their average
- Isosceles trapezoids have equal legs and base angles
- Right trapezoids have one perpendicular leg simplifying calculations
- Area depends only on bases and height, not leg lengths
- Diagonal properties vary by trapezoid type
Sources & References
- Geometry - Jurgensen, Brown, Jurgensen (McDougal Littell)Standard high school geometry textbook covering quadrilaterals
- Elementary Geometry for College Students - Alexander, Koeberlein (6th Edition)College-level geometry with trapezoid properties and proofs
- Mathematical Handbook - CRC Press Standard Mathematical TablesReference for geometric formulas and calculations
Exploring more geometry? Try our free fall calculator for physics and partial pressure calculator for chemistry.
Get Custom Geometry Calculator for Your PlatformExample Geometry Calculation
Given Dimensions:
- Top width: 6 meters
- Bottom width: 10 meters
- Length: 8 meters
- Type: Isosceles trapezoid
Calculation Steps:
- Apply area formula: A = ½(b₁ + b₂) × h
- A = ½(6 + 10) × 8 = ½(16) × 8 = 64 m²
- Calculate legs: l = √(8² + 2²) = √68 = 8.25 m
- Perimeter: P = 6 + 10 + 2(8.25) = 32.5 m
Result: Area = 64 m², Perimeter = 32.5 m, Pool surface area and deck measurements
Perfect for determining concrete requirements and pool liner specifications!
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