Trapezoid Height Calculator
Calculate the height of a trapezoid using area, legs, and angles
Calculate Trapezoid Height
Method 1: Using Area and Bases
h = 2A / (a + b)
The height equals twice the area divided by the sum of both bases
Calculation Results
Enter the required values to calculate the trapezoid height
Please enter the area and both base lengths
Example Calculations
Method 1: Using Area and Bases
Given: Area = 64 cm², Base a = 21 cm, Base b = 19 cm
Formula: h = 2A / (a + b)
Calculation: h = (2 × 64) / (21 + 19) = 128 / 40 = 3.2 cm
Result: Height = 3.2 cm
Method 2: Using Leg and Angle
Given: Leg c = 10 cm, Angle α = 75°
Formula: h = c × sin(α)
Calculation: h = 10 × sin(75°) = 10 × 0.9659 = 9.659 cm
Result: Height = 9.659 cm
Method 3: Alternative Leg and Angle
Given: Leg d = 22 cm, Angle δ = 95°
Formula: h = d × sin(δ)
Calculation: h = 22 × sin(95°) = 22 × 0.9962 = 21.916 cm
Result: Height = 21.916 cm
Height Formulas
From Area & Bases
h = 2A / (a + b)
Where A is area, a and b are parallel bases
From Leg & Angle
h = c × sin(α)
Where c is leg, α is angle with base
Alternative Leg & Angle
h = d × sin(δ)
Where d is other leg, δ is its angle
Trapezoid Properties
Height is perpendicular distance between parallel bases
Height is constant across the entire trapezoid
Area = ½ × (sum of bases) × height
Legs are the non-parallel sides
Height can be found using trigonometry with legs
Quick Tips
Choose method based on known values
Area method requires both bases and area
Trigonometric methods need one leg and angle
Angles should be measured from leg to base
All three methods give the same height
Understanding Trapezoid Height
What is Trapezoid Height?
The height of a trapezoid is the perpendicular distance between its two parallel sides (bases). This vertical distance remains constant across the entire width of the trapezoid.
Calculation Methods
- •Area Method: Use area and both base lengths
- •Trigonometric: Use a leg length and its angle with a base
- •Coordinate: Calculate using vertex coordinates
Formula Derivations
From Area Formula
Area = ½(a + b) × h
Rearranging: h = 2A / (a + b)
From Trigonometry
In right triangle formed by height:
h = leg × sin(angle)
Where angle is between leg and base
Applications
- •Architecture: Roof and foundation design
- •Engineering: Cross-sectional analysis
- •Land Surveying: Area calculations