Geometry Tool
Trapezoid Calculator
Calculate the area, perimeter, heights, base lengths, and diagonals of a trapezoid (trapezium) with input parameters. Supports isosceles and general trapezoids.
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Interactive Trapezoid Calculator Workspace
Legs (Optional for Perimeter)
Calculated Area & Perimeter
Trapezoid Area100.0000
PerimeterEnter Leg C & D
Step-by-Step Explanation
1. Add the parallel bases: 10 + 15 = 25
2. Multiply by Height, then divide by 2: ((10 + 15) ÷ 2) × 8 = 100.0000
Mathematical Formula & Variables
Equation Model
Area = ((Base a + Base b) ÷ 2) × HeightFinds the flat space enclosed by a 4-sided polygon with at least one pair of parallel sides (the bases).
Variable Definitions
| Symbol | Description |
|---|---|
| a (Base A) | The length of the parallel top flat base. |
| b (Base B) | The length of the parallel bottom flat base. |
| h (Height) | The perpendicular vertical distance between the two parallel bases. |
| c, d (Legs) | The two slanted, non-parallel side boundary lines. |
How to Use the Trapezoid Calculator
- Input the lengths of Base A and Base B.
- Input the vertical perpendicular Height of the trapezoid.
- Optionally, input Slanted Leg C and Slanted Leg D to calculate the full perimeter.
- Analyze the calculated Area and Perimeter with full mathematical breakdowns.
Practical Example Calculation
Scenario Context: A surveyor measures a trapezoidal plot of land. Base A is 100 meters, Base B is 150 meters, and the perpendicular height is 40 meters.
Step 1: Identify inputs: Base a = 100 m, Base b = 150 m, Height h = 40 m.
Step 2: Calculate Average Base: (a + b) ÷ 2 = (100 + 150) ÷ 2 = 250 ÷ 2 = 125 m.
Step 3: Calculate Area (A): A = Average Base × Height = 125 × 40 = 5,000 square meters.
The area of the trapezoidal plot is 5,000.00 square meters.
Frequently Asked Questions
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