Trapezoid Calculator
Calculate area, perimeter, and other properties of a trapezoid
Calculation Results
Enter trapezoid measurements to calculate all properties.
Type:
Base 1 (b₁): units
Base 2 (b₂): units
Height (h): units
Area (A): square units
Perimeter (P): units
Median (m): units
Leg 1: units
Leg 2: units
Angles: °, °
Trapezoid Diagram
Trapezoid Formulas
Key Properties
- Bases (b₁, b₂): The two parallel sides of the trapezoid
- Legs: The non-parallel sides
- Height (h): Perpendicular distance between the bases
- Area (A): Space contained within the trapezoid
- Perimeter (P): Sum of all sides
- Median (m): Midsegment parallel to the bases
- Angles: Two pairs of adjacent angles that are supplementary
Calculation Formulas
- Area (A): A = ½ × (b₁ + b₂) × h
- Perimeter (P): P = b₁ + b₂ + leg₁ + leg₂
- Median (m): m = ½ × (b₁ + b₂)
- Height from area: h = 2A / (b₁ + b₂)
- Leg length (right trapezoid): leg = √(h² + (b₂ - b₁)²)
- Angles (isosceles trapezoid): α = arccos[(b₂ - b₁) / (2 × leg)]
Where: b₁ = length of first base, b₂ = length of second base, h = height, leg = non-parallel side length
Example Calculation
For a trapezoid with:
Base 1 (b₁) = 8 units, Base 2 (b₂) = 12 units, Height (h) = 5 units, Legs = 5.39 units each (isosceles trapezoid).Calculations:
- Area = ½ × (8 + 12) × 5 = 50 units²
- Perimeter = 8 + 12 + 5.39 + 5.39 ≈ 30.78 units
- Median = ½ × (8 + 12) = 10 units
- Angles ≈ 68.2° and 111.8° (isosceles trapezoid)
About Trapezoids
A trapezoid is a quadrilateral with at least one pair of parallel sides called bases. The non-parallel sides are called legs. In an isosceles trapezoid, the legs are congruent and the base angles are equal.
Real-World Applications
- Architecture: Trapezoidal windows and roof designs
- Engineering: Trapezoidal threads in screws
- Design: Trapezoidal shapes in furniture and packaging
- Mathematics: Study of quadrilaterals and their properties
Types of Trapezoids
- Right Trapezoid: Has two right angles
- Isosceles Trapezoid: Non-parallel sides (legs) are congruent
- Scalene Trapezoid: No sides are equal and no angles are equal
Trapezoid Components
Bases (b₁, b₂)
Parallel sides
Height (h)
Perpendicular distance
Legs
Non-parallel sides
Area (A)
A = ½(b₁ + b₂)h
Perimeter (P)
Sum of all sides
Median (m)
m = ½(b₁ + b₂)
How to Use the Trapezoid Calculator
The Trapezoid Calculator helps compute various properties based on input values. Here's how to use it:
1. Select Calculation Method
Choose what measurements you know:
- Bases & Height - Enter both bases and height
- All Four Sides - When you know all side lengths
- Area & Height - To find the bases
- Median & Height - When you know the median length
- Legs & Bases - For calculating height and angles
2. Enter Your Values
Input positive numbers in the appropriate fields:
Example 1: Base 1 = 8, Base 2 = 12, Height = 5
Example 2: All sides = 5, 8, 5, 10 (isosceles trapezoid)
3. Get Results
The calculator will compute all properties:
- Base lengths (b₁, b₂)
- Height (h)
- Area (A)
- Perimeter (P)
- Median (m)
- Leg lengths
- Angles (for isosceles trapezoids)
Practical Applications
- Calculate material needed for trapezoidal structures
- Determine paint required for trapezoidal surfaces
- Find land area with trapezoidal plots
- Solve geometry problems involving trapezoids
Trapezoid Formulas
| Parameter | Formula | Description |
|---|---|---|
| Area (A) | ½ × (b₁ + b₂) × h | Space contained within the trapezoid |
| Perimeter (P) | b₁ + b₂ + leg₁ + leg₂ | Sum of all sides |
| Median (m) | ½ × (b₁ + b₂) | Midsegment parallel to bases |
| Height from area | h = 2A / (b₁ + b₂) | Height calculated from area |
| Leg length (right trapezoid) | √(h² + (b₂ - b₁)²) | Length of non-parallel side |
| Angles (isosceles) | α = arccos[(b₂ - b₁) / (2 × leg)] | Base angles of isosceles trapezoid |
Frequently Asked Questions
A parallelogram has two pairs of parallel sides, while a trapezoid has exactly one pair of parallel sides (in the US definition; some countries define trapezoid as having at least one pair).
For an isosceles trapezoid, you can use the formula: h = √(leg² - [(b₂ - b₁)/2]²). For other trapezoids, you typically need more information like angles or area.
Yes, a right trapezoid has two right angles. These are always adjacent to each other and connected to the same base.