Right Trapezoid Calculator
Calculate area, perimeter, sides, angles, and median of a right trapezoid
Enter Trapezoid Dimensions
Enter any three dimensions to calculate all trapezoid properties
The longer parallel side
The shorter parallel side
The perpendicular side (height)
The diagonal side
Calculated Dimensions
Properties
Example Calculation
Right Trapezoid with a = 10, b = 6, c = 5
Given: Longer base (a) = 10 units, Shorter base (b) = 6 units, Height (c) = 5 units
Step 1: Calculate slant side: d = √[(a - b)² + c²] = √[(10 - 6)² + 5²] = √[16 + 25] = √41 ≈ 6.40 units
Step 2: Calculate area: A = (a + b) × h / 2 = (10 + 6) × 5 / 2 = 40 sq units
Step 3: Calculate perimeter: P = a + b + c + d = 10 + 6 + 5 + 6.40 = 27.40 units
Step 4: Calculate median: m = (a + b) / 2 = (10 + 6) / 2 = 8 units
Step 5: Calculate acute angle: α = arctan(c / (a - b)) = arctan(5 / 4) = 51.34°
Right Trapezoid Properties
Has exactly two parallel sides (bases)
Contains exactly two right angles (90°)
One side is perpendicular to both bases
Height equals the perpendicular side length
Easier to calculate than general trapezoids
Key Formulas
Area
A = (a + b) × h / 2
Perimeter
P = a + b + c + d
Slant Side
d = √[(a - b)² + c²]
Median
m = (a + b) / 2
Quick Facts
A rectangle is also a right trapezoid
Cannot have just one right angle
Height = perpendicular side length
Sum of all angles = 360°
Understanding Right Trapezoids
What is a Right Trapezoid?
A right trapezoid is a special type of trapezoid that has exactly one leg perpendicular to both of its parallel bases. This means it contains exactly two right angles (90°). The perpendicular leg serves as the height of the trapezoid, making calculations much simpler than for general trapezoids.
Key Components
- •Longer Base (a): The longer of the two parallel sides
- •Shorter Base (b): The shorter of the two parallel sides
- •Height (c): The perpendicular side (also the trapezoid's height)
- •Slant Side (d): The non-perpendicular leg connecting the bases
Calculation Methods
Area Formula
A = (a + b) × h / 2
Average of parallel sides times height
Pythagorean Relationships
d = √[(a - b)² + c²]
Used to find missing side lengths
Angle Calculations
α = arctan(c / (a - b))
Find acute angle at slant side
Median (Midsegment)
m = (a + b) / 2
Line parallel to bases through midpoint