Area of a Trapezoid
A trapezoid has two parallel sides called the bases. Its area depends on the average of those bases and the height between them.
Method
- Identify the two bases: the parallel sides are usually labeled (b_1) and (b_2).
- Find the height: this is the perpendicular distance between the bases, not the slanted side.
- Use the area rule:
[
A=\frac{(b_1+b_2)h}{2}
]
- Simplify carefully: combine like terms, reduce fractions, and write the final answer in simplest form.
Example structure
- Add the two bases.
- Multiply by the height.
- Divide by 2.
Check your work
- Make sure the height is perpendicular to both bases.
- If the trapezoid looks like a rectangle or triangle in special cases, the result should still match the formula.
- The area should have square units.
This method works for every trapezoid area exercise: identify the bases, use the perpendicular height, apply the formula, and simplify the result.