Isosceles Trapezoid Calculator
Calculate area, perimeter, height, diagonals, and angles of isosceles trapezoids
Calculate Isosceles Trapezoid Properties
Note: Enter at least 2 known values to calculate all properties. Leave unknown fields empty.
The longer of the two parallel sides
The shorter of the two parallel sides
Length of the two equal non-parallel sides
Perpendicular distance between the parallel sides
Trapezoid Properties
Enter at least 2 known values to calculate all trapezoid properties.
Example Calculation
Example: Garden Trapezoid Plot
Problem: A garden plot is shaped like an isosceles trapezoid with bases of 12m and 8m, and legs of 5m each.
Given: Longer base (a) = 12m, Shorter base (b) = 8m, Leg (c) = 5m
Find: Height, Area, and Perimeter
Solution
Step 1 - Calculate Height:
h = √[c² - ((a-b)/2)²] = √[5² - ((12-8)/2)²] = √[25 - 4] = √21 = 4.58m
Step 2 - Calculate Area:
A = ½(a + b) × h = ½(12 + 8) × 4.58 = ½ × 20 × 4.58 = 45.8m²
Step 3 - Calculate Perimeter:
P = a + b + 2c = 12 + 8 + 2(5) = 30m
Key Formulas
Area
A = ½(a + b) × h
Perimeter
P = a + b + 2c
Height
h = √[c² - ((a-b)/2)²]
Leg Length
c = √[h² + ((a-b)/2)²]
Midsegment
m = (a + b)/2
Isosceles Trapezoid Properties
Two equal legs (non-parallel sides)
Two parallel bases of different lengths
Base angles are equal
Diagonals are equal in length
Has one line of symmetry
Opposite angles are supplementary
Common Applications
Architecture and construction
Bridge and roof designs
Land surveying and plots
Engineering calculations
Geometric problem solving
Understanding Isosceles Trapezoids
What is an Isosceles Trapezoid?
An isosceles trapezoid is a special type of trapezoid where the non-parallel sides (legs) have equal length. This creates a symmetric shape with useful mathematical properties that make calculations more predictable and structured.
Key Characteristics
- •Equal legs: Both non-parallel sides have the same length
- •Parallel bases: Two sides are parallel but of different lengths
- •Equal base angles: Angles adjacent to each base are equal
- •Equal diagonals: Both diagonals have the same length
Mathematical Relationships
Area Formula
The area is calculated as the average of the two parallel sides multiplied by the height:A = ½(a + b) × h
Height Calculation
When you know the bases and leg length, the height can be found using:h = √[c² - ((a-b)/2)²]
Angle Relationships
Adjacent angles are supplementary (add up to 180°), and base angles are equal.
Real-World Applications
Architecture
Used in building facades, window designs, and decorative elements where symmetry is important.
Engineering
Common in bridge designs, dam cross-sections, and structural elements requiring stability.
Land Planning
Used for property boundaries, garden plots, and urban planning where symmetric shapes are needed.