A trapezoid is a four-sided shape with one pair of parallel sides — think of a tapering lot, a hip-roof plane, or a garden bed that narrows. Its area formula is beautifully simple once you know which sides to use. This guide makes it clear.
What’s in this guide
The trapezoid area formula
Parallel sides and height
Identify the two parallel sides (a and b) — the ones that stay the same distance apart. The height is the straight perpendicular distance between them, which is usually shorter than the slanted legs.
Measure straight across between the parallel sides, at a right angle — not along a sloped edge.
Worked example
A garden bed with a 10 ft top, an 18 ft bottom, and 8 ft of depth:
| Step | Value |
|---|---|
| Add parallel sides | 10 + 18 = 28 ft |
| Average (÷ 2) | 28 ÷ 2 = 14 ft |
| Multiply by height | 14 × 8 = 112 sq ft |
Where trapezoids appear
| Application | Trapezoid role |
|---|---|
| Tapering lots | Front wider than back (or vice versa) |
| Hip roof planes | Trapezoidal roof faces |
| Retaining walls | Cross-sections |
| Garden & patio beds | Narrowing shapes |
| Driveways | Flared entrances |
Common mistakes
The height is the perpendicular distance between the parallel sides, not a leg length.
Only the two parallel sides are averaged. The slanted legs don't enter the area formula.
(a + b) × h without halving doubles the area.
Key takeaways
- Trapezoid area = ½ × (a + b) × height.
- a and b are the two parallel sides.
- Height is the perpendicular distance between them.
- It equals a rectangle with the average width.
Related calculators & guides
Frequently asked questions
- How do I calculate the area of a trapezoid?
- Average the two parallel sides and multiply by the height between them: area = ½(a + b) × h. With parallel sides of 10 ft and 18 ft and a height of 8 ft, area = ½(28) × 8 = 112 sq ft.
- Which sides are the parallel sides?
- The two sides that never meet, no matter how far extended — usually the top and bottom. They are labeled a and b in the formula. The height is the perpendicular distance between them.
- What is the height of a trapezoid?
- The perpendicular (straight-across) distance between the two parallel sides — not the length of the slanted legs.
- Why does the formula use the average of the two sides?
- A trapezoid is like a rectangle whose width is the average of its two parallel sides. Averaging them and multiplying by height gives the same area exactly.