Case 1
- First parallel side (a)
- 8
- Second parallel side (b)
- 4
- Height (h)
- 5
30.00
Open with these valuesTrapezoid Area Calculator
30.00square units
Result: 30.00 square unitsAverage the two parallel sides and multiply by how far apart they are. Sides of 8 and 4 at a height of 5 give 6 × 5 = 30 square units. The two slanted legs never enter the formula, and the order of the parallel sides does not matter.
The numbers at a glance
Held fixed: First parallel side (a) 8.000, Second parallel side (b) 4.000.
| Height (h) | Result |
|---|---|
| 2.000 | 12.00 |
| 4.000 | 24.00 |
| 5.000Your value | 30.00 |
| 6.000 | 36.00 |
| 8.000 | 48.00 |
| 10.000 | 60.00 |
Worked examples
Case 2
- First parallel side (a)
- 10
- Second parallel side (b)
- 10
- Height (h)
- 4
40.00
Open with these valuesCase 3
- First parallel side (a)
- 12
- Second parallel side (b)
- 8
- Height (h)
- 10
100.00
Open with these valuesHow it's calculated
A = ((a + b) ÷ 2) × h
- StepEnter the two sides that run parallel to each other, in any order.
- StepMeasure the height straight across between them, at a right angle.
- ResultRead the area in the square of the unit you entered.
What this number means
The two legs never enter the formula
Only the pair of sides that run parallel to each other belongs in a and b. The slanted legs are not used at all, however carefully you measured them.
Height means the gap between the parallels
Measure straight across from one parallel side to the other, at a right angle. A sloping leg is longer than that gap; if it is all you have, work the perpendicular height out with trigonometry first.
The order of a and b makes no difference
Sides of 8 and 4 at a height of 5 give 30 square units, and so do 4 and 8. The formula averages the two, and addition is commutative.
Trapezoid, trapezium, Trapez
US usage says trapezoid, UK usage trapezium, German Trapez — the shape with one pair of parallel sides is meant in each case. The formula ((a + b) ÷ 2) × h is identical either way.
Commonly misread
The slanted leg measures 5, so the height is 5.
The height is the perpendicular distance between the two parallel sides, not the length of a leg. A sloping leg is longer and pushes the area up.
Any two of the four sides can go in as a and b.
Only the pair that is parallel. The legs play no part in ((a + b) ÷ 2) × h.
Add the two parallel sides and multiply by the height.
That skips the halving and doubles the answer. For 8, 4 and 5 it gives 60 where the area is 30 square units.
Reference table
| a, b, h | Worked out | Area |
|---|---|---|
| 5, 3, 2 | (5 + 3) ÷ 2 × 2 | 8 |
| 6, 2, 3 | (6 + 2) ÷ 2 × 3 | 12 |
| 8, 4, 5 | (8 + 4) ÷ 2 × 5 | 30 |
| 10, 10, 4 | (10 + 10) ÷ 2 × 4 | 40 |
| 12, 8, 10 | (12 + 8) ÷ 2 × 10 | 100 |
Questions
How do I calculate the area of a trapezoid?
Add the two parallel sides, halve the total, then multiply by the perpendicular height. For parallel sides of 8 and 4 and a height of 5, that is 6 × 5 = 30 square units. In essence you average the two parallel sides and multiply by how far apart they are.
Which measurement is the height?
The perpendicular distance between the two parallel sides — the straight-across gap measured at a right angle, not the length of a slanted leg. If you only have a sloping side, work out the perpendicular height first with trigonometry.
Which two sides do I enter as a and b?
The two sides that are parallel to each other, sometimes called the bases. The other two sides, the legs, are not used in this formula. Their order does not matter, because addition is commutative.
What is the difference between a trapezoid and a trapezium?
They describe the same shape under different naming conventions: US usage says trapezoid, UK usage says trapezium, and German says Trapez. The formula ((a + b) ÷ 2) × h is identical either way. This calculator works for all three terms.
What units does the result use?
It is unit-agnostic. Enter both parallel sides and the height in one length unit and the area comes back in square units of that unit. A metre side with a foot height would give a meaningless result.
Sources and last check
Information, not professional advice.