A trapezoid has one pair of parallel sides, called its bases. The same trick that worked for the triangle, two copies make a parallelogram, works here too.
Key idea
The area of a trapezoid is $A = \frac{1}{2}(b_1 + b_2)h$: add the two parallel sides, multiply by the height, and take half.
Why it works
Put a copy of the trapezoid next to it, turned upside down. The long base of one lines up with the short base of the other, so together they make a parallelogram with base $b_1 + b_2$ and the same height. Its area is $(b_1 + b_2)h$, and the trapezoid is half of it.
Worked example: Use the formula
A trapezoid has bases 10 ft and 6 ft and height 4 ft. Find its area.
- Add the bases: $10 + 6 = 16$.
- Multiply by the height: $16 \times 4 = 64$.
- Take half: $32$.
Answer: 32 square feet
Worked example: With decimals
Find the area of a trapezoid with bases 7.5 m and 4.5 m and height 3 m.
- $7.5 + 4.5 = 12$.
- $\frac{1}{2} \times 12 \times 3 = 18$.
Answer: 18 square meters
Worked example: Another way: split it
A trapezoid has bases 9 and 5 and height 4, with its slanted side on the right. Split it into a rectangle and a triangle.
- Rectangle: $5 \times 4 = 20$.
- Triangle: base $9 - 5 = 4$, height 4: $\frac{1}{2} \times 4 \times 4 = 8$.
- Total $20 + 8 = 28$. The formula agrees: $\frac{1}{2}(9 + 5) \times 4 = 28$.
Answer: 28 square units
Common mistake
Using a slanted side instead of the height, or adding all four sides. Only the two parallel sides go in the formula, and the height must be straight across between them. Quick check: the area must be between $b_2 \times h$ and $b_1 \times h$ (for the first example, between $6 \times 4 = 24$ and $10 \times 4 = 40$).