Trapezoid Calculator
Calculate area, perimeter, height, midsegment, and diagonals of any trapezoid
Perpendicular distance between the parallel bases
Enter leg lengths to calculate perimeter
Height will be calculated from the area and bases
In an isosceles trapezoid, both legs have equal length
Trapezoid Properties
Area
Perimeter
Height
Midsegment
Top Base (a)
Bottom Base (b)
Left Leg (c)
Right Leg (d)
Diagonal
Both diagonals equal
Base Angle
°
Angle at each base corner
Top Angle
°
Angle at each top corner
Type
Isosceles
Equal legs & angles
Trapezoid Formulas
Area
A = ½(a + b) × h
Perimeter
P = a + b + c + d
Midsegment
m = (a + b) / 2
Height from Area
h = 2A / (a + b)
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About Trapezoid Calculator
What is a Trapezoid?
A trapezoid (called a trapezium in British English) is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases (often labeled a and b), while the non-parallel sides are called legs (labeled c and d). The perpendicular distance between the bases is the height (h).
Trapezoids are commonly found in architecture, engineering, and everyday objects like tables, lamp shades, and highway signs.
Types of Trapezoids
General Trapezoid
A trapezoid with no special properties—the legs can have different lengths and the base angles are not necessarily equal.
Isosceles Trapezoid
A trapezoid where the legs are equal in length (c = d). This creates symmetry: the base angles are equal, and the diagonals are equal in length.
Right Trapezoid
A trapezoid where two adjacent angles are right angles (90°). One leg is perpendicular to both bases.
How to Use This Calculator
From Dimensions Mode
- Select From Dimensions mode
- Enter the top base (a) and bottom base (b)
- Enter the height (h)
- Optionally enter the leg lengths (c and d) for perimeter calculation
- View all calculated properties instantly
From Area Mode
- Select From Area mode
- Enter the known area
- Enter the two base lengths
- The calculator determines the height and other properties
Isosceles Mode
- Select Isosceles mode
- Enter the top base (a) and bottom base (b)
- Enter the leg length
- The calculator computes height, area, diagonals, and all other properties
Trapezoid Formulas
Core Formulas
| Property | Formula | Description |
|---|---|---|
| Area | A = ½(a + b) × h | Half the sum of bases times height |
| Perimeter | P = a + b + c + d | Sum of all four sides |
| Midsegment | m = (a + b) / 2 | Also called median; connects midpoints of legs |
| Height from Area | h = 2A / (a + b) | Derived from the area formula |
Isosceles Trapezoid Formulas
| Property | Formula |
|---|---|
| Leg Length | c = √[h² + ((b-a)/2)²] |
| Height from Leg | h = √[c² - ((b-a)/2)²] |
| Diagonal | d = √[c² + a×b] |
| Base Angle | θ = arctan(2h / (b-a)) |
Understanding Trapezoid Properties
The Midsegment (Median)
The midsegment connects the midpoints of the two legs. Its length equals the average of the two bases: m = (a + b) / 2. The area can also be expressed as A = m × h.
Diagonals
In a general trapezoid, the diagonals are usually different lengths. In an isosceles trapezoid, they are equal. The diagonals intersect each other in a specific ratio related to the base lengths.
Height Calculation
For an isosceles trapezoid, if you know the bases and leg length, the height can be calculated using the Pythagorean theorem:
h = √[c² - ((b-a)/2)²]
Real-World Applications
Architecture & Construction
- Roof trusses and gable ends
- Window and door frames
- Retaining walls
- Bridge supports
Engineering
- Cross-sections of channels and ducts
- Gear tooth profiles
- Structural beam calculations
Everyday Objects
- Table tops
- Lamp shades
- Flower pots
- Highway signs
- Computer keyboard keys
Frequently Asked Questions
What's the difference between a trapezoid and a parallelogram?
A trapezoid has exactly one pair of parallel sides, while a parallelogram has two pairs of parallel sides. A parallelogram can be considered a special case where both pairs of opposite sides are parallel.
How do I find the area if I only know the four sides?
For a general trapezoid with sides a, b, c, d (where a and b are parallel), use:
A = [(a+b)/2] × √[c² - ((a-b+c²-d²)/(2(a-b)))²]
This is known as the Bretschneider formula adapted for trapezoids. However, it's easier to measure the height directly when possible.
Can a trapezoid have two right angles?
Yes! This is called a right trapezoid. It has two right angles on the same leg, meaning one leg is perpendicular to both parallel sides.
What is an isosceles trapezoid?
An isosceles trapezoid has legs of equal length (c = d). This creates symmetry: the base angles are equal (both acute angles are equal, both obtuse angles are equal), and the diagonals are equal in length.
Why is the midsegment important?
The midsegment (median) is useful because its length equals the average of the two bases, and the area equals the midsegment times the height: A = m × h. This makes it a convenient reference line for calculations.
Important Notes
- The height must be measured perpendicular to the bases, not along a leg
- In an isosceles trapezoid, the formula h = √[c² - ((b-a)/2)²] requires that the leg length c is greater than half the difference of the bases
- This calculator assumes the bases are the parallel sides; enter the shorter base as 'a' and longer as 'b' for consistency
Note: This calculator provides mathematical results for geometric shapes. For engineering or construction projects, always consult with qualified professionals and verify measurements.