Area of a Trapezoid Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the area of a trapezoid?
Answer
Area of a trapezoid
A = ½ · (a + b) · h
Here a is the side (or base), b is the second side, h is the height, perpendicular to the base. The result comes out in square units.
Where the formula comes from
A = ½ · (a + b) · h
Join a second copy of the trapezoid upside down to the first: together they form a parallelogram whose base is a + b and whose height is h. One trapezoid is half of that. In other words: the average of the two parallel sides, times the height.
Worked examples
Let a = 10, b = 6, h = 4. Then the area of a trapezoid = 32 square units.
Let a = 7.5, b = 3.5, h = 5. Then the area of a trapezoid = 27.5 square units.
The common mistake
Adding the slanted sides instead of the parallel ones. Only the two parallel sides go into a + b; the legs do not enter the area formula at all.
Related Calculations
See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
Geometry Formulas: Area, Volume, Perimeter
These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the area of a trapezoid? (The answer is: A = ½ · (a + b) · h). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Values from the Formula (b = 6, h = 4)
| If a = | Area |
|---|---|
| 1 | 14 square units |
| 2 | 16 square units |
| 3 | 18 square units |
| 4 | 20 square units |
| 5 | 22 square units |
| 10 | 32 square units |
FAQ
What is the formula for the area of a trapezoid?
Area of a trapezoid A = ½ · (a + b) · h
Where does this formula come from?
Join a second copy of the trapezoid upside down to the first: together they form a parallelogram whose base is a + b and whose height is h. One trapezoid is half of that. In other words: the average of the two parallel sides, times the height.
What is the most common mistake here?
Adding the slanted sides instead of the parallel ones. Only the two parallel sides go into a + b; the legs do not enter the area formula at all.
How do I use this formula?
Put your own numbers in place of the letters. With a = 7.5, b = 3.5, h = 5, for instance, the formula A = ½ · (a + b) · h gives = 27.5 square units.
See Also
- Area of a Circle Formula
- Area of a Hexagon Formula
- Area of a Parallelogram Formula
- Area of a Regular Polygon Formula
- Area of a Rectangle Formula
- Area of a Rhombus Formula
- Area of a Circular Sector Formula
- Area of a Square Formula
- Area of a Triangle Formula
- Circumference of a Circle Formula
- Diameter of a Circle Formula
- Perimeter of a Regular Polygon Formula
- Perimeter of a Rectangle Formula
- Perimeter of a Semicircle Formula
- Perimeter of a Square Formula
- Perimeter of a Triangle Formula
- Surface Area of a Cone Formula
- Surface Area of a Cube Formula
- Площадь трапеции
- Área del trapecio
- Área do trapézio