Area of a Trapezoid Calculator
Calculate the area, perimeter, and properties of trapezoids using parallel bases and height
Calculate Trapezoid Properties
One of the parallel sides
The other parallel side
Perpendicular distance between parallel bases
Trapezoid Properties
Formulas Used:
Area: A = (a + b) × h / 2
Median: m = (a + b) / 2
Calculation: (0 + 0) × 0 / 2
Example Calculation
Garden Bed Trapezoid
Given: Base A = 8 meters, Base B = 4 meters, Height = 5 meters
Find: Area and median of the trapezoid
Solution
Area: A = (a + b) × h / 2 = (8 + 4) × 5 / 2 = 30 m²
Median: m = (a + b) / 2 = (8 + 4) / 2 = 6 m
Result: The trapezoid has an area of 30 square meters
Trapezoid Formulas
Area
A = (a + b) × h / 2
Where a, b are parallel bases and h is height
Perimeter
P = a + b + c + d
Sum of all four sides
Median (Midsegment)
m = (a + b) / 2
Average of parallel bases
Trapezoid Properties
Has exactly one pair of parallel sides (bases)
Sum of interior angles equals 360°
Adjacent angles are supplementary (sum to 180°)
Median connects midpoints of non-parallel sides
Median is parallel to bases and equals their average
Understanding Trapezoids and Area Calculation
What is a Trapezoid?
A trapezoid is a quadrilateral (4-sided polygon) with exactly one pair of parallel sides called bases. The non-parallel sides are called legs. The perpendicular distance between the parallel bases is the height.
Key Components
- •Bases (a, b): The two parallel sides
- •Legs (c, d): The two non-parallel sides
- •Height (h): Perpendicular distance between bases
- •Median: Line segment connecting midpoints of legs
Area Formula Derivation
The trapezoid area formula comes from the average of the two parallel bases multiplied by the height:
A = (a + b) × h / 2
This can be understood as the area of a rectangle with width equal to the average of the bases: (a + b)/2, and height h.
Special Case: When a = b, the trapezoid becomes a rectangle, and the formula simplifies to A = a × h.
Types of Trapezoids
Scalene Trapezoid
All sides have different lengths. No special symmetry properties.
Isosceles Trapezoid
Both legs have equal length. Has line symmetry and equal base angles.
Right Trapezoid
Has two adjacent right angles. One leg is perpendicular to both bases.