Trapezoid area tutorial
A trapezoid has exactly one pair of parallel sides called the bases. The area formula takes the average of those two bases and multiplies by the perpendicular height. One formula handles every trapezoid — no matter how slanted the non-parallel sides are.
Core formula
Area: $A = \dfrac{1}{2}(b_1 + b_2)\,h$
where $b_1$ and $b_2$ are the two parallel bases and $h$ is the perpendicular height between them.
Anatomy of a trapezoid
Label the shorter parallel side $b_1$ and the longer parallel side $b_2$. The height $h$ is the perpendicular distance between the two bases — it is measured straight across, not along the slanted leg.
Think of the trapezoid as a rectangle with average width $\dfrac{b_1 + b_2}{2}$ and height $h$. The area is that rectangle's area.
Why the formula works
The trapezoid area formula is really just the average-base × height idea:
$$A = \underbrace{\frac{b_1 + b_2}{2}}_{\text{average base}} \times h$$
You can also rearrange to isolate the height or solve for a missing base:
Isolate h (know A, b₁, b₂)
$h = \dfrac{2A}{b_1 + b_2}$
Isolate b₁ (know A, b₂, h)
$b_1 = \dfrac{2A}{h} - b_2$
Step-by-step checklist
- Identify the two parallel sides. Label the shorter one $b_1$ and the longer one $b_2$.
- Identify the perpendicular height $h$ — not the slanted leg length.
- Add the two bases: $b_1 + b_2$.
- Divide by 2 to get the average base.
- Multiply by $h$.
- Write your answer with the correct units (units² for area).
Worked example
A trapezoid has parallel bases of 6 and 10, and a perpendicular height of 5. Find the area.
Step 1 — Add the bases: $6 + 10 = 16$
Step 2 — Average the bases: $16 \div 2 = 8$
Step 3 — Multiply by height: $8 \times 5 = 40$
Area = 40 square units
A second example — find the height
A trapezoid has an area of 42 square units and parallel bases of 6 and 8. Find the height.
Rearranged formula: $h = \dfrac{2A}{b_1 + b_2}$
Substitute: $h = \dfrac{2 \times 42}{6 + 8} = \dfrac{84}{14} = 6$
Height = 6 units
Try a sample problem
Use the formula above to answer the question. Click Check answer to see the worked solution.