Take two identical trapezoids and turn one upside down. Together they fit into a parallelogram.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The base of that parallelogram
Its base is the two parallel sides added: a + b.
One trapezoid is half of it
The parallelogram is (a + b) × h. One trapezoid is half that, so divide by 2.
The formula
Area = (a + b) × h ÷ 2. The height is perpendicular, as always.
Two copies make a parallelogram
Take a second copy of the trapezoid, turn it upside down and join it to the first. The result is a parallelogram whose base is the sum of the two parallel sides. Its area is (a + b) × h, so one trapezoid is half that.
The formula, and how to read it
Area = (a + b) ÷ 2 × h. The (a + b) ÷ 2 part is the average of the two parallel sides, so the formula says: area equals the average width times the height. Read that way it is much easier to remember than as symbols.
Only the parallel sides go in the formula
The a and b are the two parallel sides. The slanted sides do not appear at all. Substituting a slanted side is a common error, and identifying the parallel pair before calculating prevents it.
Check with a special case
If a and b are equal, the shape is a parallelogram and the formula gives a × h — correct. If b is zero, the shape is a triangle and the formula gives a × h ÷ 2 — also correct. A formula that degrades correctly is a formula you can trust.
Step 2: Try It Yourself
Tap and try it out.
Area · squares inside
40
Perimeter · walk around
28
10 × 4 = 40 · 10 + 4 + 10 + 4 = 28
Area counts the squares inside. Perimeter measures the walk all the way round.
Step 3: Watch an Example
One step at a time.
Watch Leo Find a Trapezoid Area
Parallel sides 6 and 10, height 4.
- Step 1
He adds the parallel sides: 6 + 10 = 16.
Step 4: Your Turn
Practice makes it stick.
The Garden Bed
Problem 1 of 2
Parallel sides 4 and 8, height 3. What is the area?
The Roof Panel
Problem 2 of 2
Parallel sides 5 and 9, height 6. What is the area?
Add, Multiply, Halve
1 of 4
Parallel sides 3 and 7, height 2. Area?
2 of 4
Parallel sides 6 and 6, height 5. Area?
3 of 4
Parallel sides 2 and 8, height 4. Area?
4 of 4
Why is the answer halved at the end?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Parallel sides 5 and 11, height 4. Area?
What You Learned
- Two identical trapezoids make a parallelogram.
- Its base is the two parallel sides added together.
- Area = (a + b) × h ÷ 2.