Trapezoid Perimeter Calculator
Calculate the perimeter of a trapezoid using sides, angles, and height
Calculate Trapezoid Perimeter
Method 1: Direct Calculation
First parallel side
Second parallel side
First oblique side
Second oblique side
P = a + b + c + d
Sum of all four sides
Calculation Results
Enter the required values to calculate the trapezoid perimeter
Please enter all four side lengths
Example Calculations
Example 1: Direct Method
Given: Base a = 10 cm, Base b = 6 cm, Side c = 5 cm, Side d = 4 cm
Formula: P = a + b + c + d
Calculation: P = 10 + 6 + 5 + 4 = 25 cm
Result: Perimeter = 25 cm
Example 2: Using Angles
Given: Side c = 4 cm, Side d = 3 cm, Base a = 10 cm, Angle α = 30°
Step 1: Calculate height: h = c × sin(30°) = 4 × 0.5 = 2 cm
Step 2: Calculate projections: c_proj = 4 × cos(30°) = 3.46 cm
Step 3: Find base b: b = a - projections = 10 - 3.46 - 2.24 = 4.3 cm
Step 4: P = 10 + 4.3 + 4 + 3 = 21.3 cm
Example 3: Isosceles Trapezoid
Given: Base a = 12 cm, Base b = 8 cm, Side c = 5 cm (equal sides)
Formula: P = a + b + 2c (since c = d in isosceles)
Calculation: P = 12 + 8 + 2(5) = 12 + 8 + 10 = 30 cm
Result: Perimeter = 30 cm
Perimeter Formulas
General Trapezoid
P = a + b + c + d
Sum of all four sides
Isosceles Trapezoid
P = a + b + 2c
c = d (equal oblique sides)
Using Trigonometry
h = c × sin(α)
projection = c × cos(α)
For advanced calculations
Trapezoid Elements
Bases (a, b)
Parallel sides of the trapezoid
Legs (c, d)
Non-parallel oblique sides
Height (h)
Perpendicular distance between bases
Angles
Interior angles sum to 360°
Quick Tips
Perimeter is the sum of all four sides
In isosceles trapezoids, the oblique sides are equal
Use trigonometry when you have angles and one side
Height helps calculate missing sides using projections
Adjacent angles are supplementary (sum to 180°)
Understanding Trapezoid Perimeter
What is Perimeter?
The perimeter of a trapezoid is the total distance around its outer edge. It's calculated by adding the lengths of all four sides: the two parallel bases and the two oblique legs.
Basic Formula
P = a + b + c + d
Sum of all four sides
Calculation Methods
- •Direct: When all four sides are known
- •Trigonometric: Using angles, height, and known sides
- •Coordinate: Using vertex coordinates
Special Cases
Isosceles Trapezoid
P = a + b + 2c
The oblique sides (legs) are equal in length
Right Trapezoid
One leg is perpendicular to the bases
Simplifies calculations with right angles
Applications
- •Fencing: Amount of material needed to enclose a trapezoid area
- •Architecture: Building perimeters and foundations
- •Land Surveying: Property boundary measurements