Quick answer
The area of a trapezoid is A = (a + b) ÷ 2 × h. Parallel sides of 5 and 7 with a height of 4 give (5 + 7) ÷ 2 × 4 = 24.
Enter the two parallel sides and the height. The calculator returns the area.
Related tools: Area Calculator: Area of common two-dimensional shapes. Area of a Circle Calculator: Area of a circle from its radius, diameter or circumference. Sector Area Calculator: Area and arc length of a circular sector.
How to use the Area of a Trapezoid Calculator
- Enter base a (above 0).
- Enter base b (above 0).
- Enter height (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Base a | A number | > 0 |
| Base b | A number | > 0 |
| Height | A number | > 0 |
Formula and method
Formula
A = (a + b) ÷ 2 × h
IEEE-754 double precision; shown to at most 6 decimal places.
Average of the parallel sides times the height.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Base a = 5; Base b = 7; Height = 4.
| Result | Value |
|---|---|
| Area | 24 |
Example 2
Inputs: Base a = 2.5; Base b = 3.5; Height = 2.
| Result | Value |
|---|---|
| Area | 6 |
The first line is the headline result (area). IEEE-754 double precision; shown to at most 6 decimal places.
Why it works
The area equals the average of the parallel sides times the height. Two copies of the trapezoid form a parallelogram with base a + b and height h, so each has half its area.
Height not slant
Height is the perpendicular distance between the parallel sides, not the slanted side. All values must be positive. In UK usage the shape is called a trapezium.
How the result changes with base a
Holding every other input at the first worked example, this table changes only base a. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Base a | Area |
|---|---|
| 2.5 | 19 |
| 5 | 24 |
| 10 | 34 |
| 20 | 54 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Height: entering "0" shows "Height must be greater than 0." beside that field and no result.
Choosing between the Area of a Trapezoid Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
| [Sector Area Calculator](/math/sector-area/) | radius and central angle | Sector area |
| [Surface Area Calculator](/math/surface-area-calculator/) | shape and a | Surface area |
| [Triangle Area Calculator](/math/triangle-area-calculator/) | base and height | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- All values positive
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for height to confirm this.
Frequently asked questions
What is the median of a trapezoid?
(a + b) ÷ 2, 6 here.
What if I know the slant side?
Find the height with trigonometry.
Is a parallelogram a trapezoid?
In the inclusive definition, yes.
What does the Area of a Trapezoid Calculator calculate?
Area of a trapezoid from its parallel sides and height. It returns Area.
What formula does the Area of a Trapezoid Calculator use?
A = (a + b) ÷ 2 × h. Average of the parallel sides times the height.
What do I need to enter in the area of a Trapezoid Calculator?
You enter Base a, Base b and Height.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. All values positive.
What is an example of a area of a Trapezoid result?
With base a 5, base b 7 and height 4, the area is 24.
Related calculators
- Area Calculator — Area of common two-dimensional shapes.
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Sector Area Calculator — Area and arc length of a circular sector.
- Surface Area Calculator — Surface area of a sphere, cube, cylinder, cone or box.
- Triangle Area Calculator — Area of a triangle from base and height.
- Surface Area of a Cylinder Calculator — Surface area and volume of a cylinder.
- Orthocenter Calculator — Orthocenter of a triangle from its vertices.
- Hexagon Calculator — Area, perimeter and angles of a regular 6-sided polygon.
- Pentagon Calculator — Area, perimeter and angles of a regular 5-sided polygon.
Sources
- Standard Euclidean geometry formulas (e.g. NIST Digital Library of Mathematical Functions §4, CRC Standard Mathematical Tables)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.