★ MATH · GEOMETRY · TRAPEZOID AREA
On the defaults — bases 8 and 12, height 5 — the area is 50 square units, and the midsegment is 10. Put in the two bases and the height, or switch modes to solve for a missing height or a missing base. This one is the TRAPEZOID tool — the average of the bases times the height — the area-calculator page is the GENERAL AREA tool — rectangles, circles, triangles and more — not a trapezoid specialist; the square-footage-calculator page is the ROOM SIZE tool — rooms and flooring — not a shape formula; the land-area-calculator page is the LAND tool — plots and acres — not a single shape; and the area-triangle-coordinates page is the COORDINATES tool — triangle area from points — not bases and height. No trapezoid calculator exists on this site — this one is the first.
A trapezoid’s area is the average of its two bases, times its height: (a + b) / 2 × h. Bases 8 and 12 average to 10, and 10 × 5 is 50 square units. The average of the bases is the midsegment — the line joining the midpoints of the legs. Switch modes to solve for a missing height (h = 2A / (a + b)) or a missing base (b = 2A / h − a). Base b may be 0, which is a triangle; a solved base below zero means no such trapezoid.
It means a trapezoid with bases 8 and 12 and a height of 5 covers 50 square units. The formula is the average of the two bases, times the height: (8 + 12) / 2 is 10, and 10 × 5 is 50. The average of the bases is also called the midsegment, and it is the length of the line joining the midpoints of the two legs — 10 here, the same number as the average.
The bases are the parallel sides. A trapezoid has one pair of parallel sides, and those two are the bases — a and b in the formula. The other two sides, the legs, are not in the formula at all. If you use a leg as a base, the answer is wrong; if the shape has two pairs of parallel sides it is a parallelogram, and the formula still works, because the two bases are equal.
The height is perpendicular, not slanted. The height is the straight distance between the two bases, measured at a right angle — not the length of a slanted leg. A leg is always at least as long as the height, and usually longer. If you are given a leg and not a height, you need more information — a right triangle on the side, for example — before the formula can be used.
It also runs backwards. The same formula solves for a missing height or a missing base: height is twice the area divided by the sum of the bases, and base b is twice the area divided by the height, minus base a. A solved base below zero means no such trapezoid exists — the area is too small for the base and height you gave it.
On the defaults: bases 8 and 12, height 5.
The defaults are bases 8 and 12 with a height of 5, which is an area of 50 square units and a midsegment of 10. They are a starting point, not a standard: your trapezoid may be bigger or smaller, flatter or taller, and the right answer for you is the one your numbers describe. Put your numbers in, read the answer, and check the working before you use it.
These notes repeat in every explainer section because this page is built to be read start to finish: the bases are the parallel sides; the height is perpendicular, not slanted; and the formula runs backwards for a missing height or base.
| Output | Formula | What it means |
|---|---|---|
| What to solve for | mode | Area. |
| Base a | input | 8. |
| Base b | input | 12. |
| Height | input | 5. |
| Area | input | 50. |
| Answer | (a + b) / 2 × h | 50. |
| Midsegment | (a + b) / 2 | 10. |
| Verdict | in words | With bases 8 and 12 and a height of 5, the trapezoid’s area is 50 square units. |
| Reverse: Smallest whole height for area 50 or more (bases 8 and 12) | step | 5: Area 50 square units (50.000000 unrounded), midsegment 10. |
| Reverse: Smallest whole base b for area 50 or more (base a 8, height 5) | step | 12: Area 50 square units (50.000000 unrounded), midsegment 10. |
| Reverse: Largest whole base a for area 60 or less (base b 12, height 6) | step | 8: Area 60 square units (60.000000 unrounded), midsegment 10. |
| Reverse: Smallest whole height for area 100 or more (bases 10 and 20) | step | 7: Area 105 square units (105.000000 unrounded), midsegment 15. |
| Reverse: Largest whole height for area 50 or less (bases 8 and 12) | step | 5: Area 50 square units (50.000000 unrounded), midsegment 10. |
| Reverse: Smallest whole height for area 60 or more (bases 7.5 and 12.5) | step | 6: Area 60 square units (60.000000 unrounded), midsegment 10. |
| Bases 8 and 12, height 5 | same model | Area 50 square units (50.000000 unrounded), midsegment 10. |
| Bases 10 and 6, height 4 | same model | Area 32 square units (32.000000 unrounded), midsegment 8. |
| Bases 7.5 and 12.5, height 6 | same model | Area 60 square units (60.000000 unrounded), midsegment 10. |
| Height from area 50, bases 8 and 12 | same model | Height 5 (5.000000 unrounded), midsegment 10. |
| Height from area 84, bases 9 and 15 | same model | Height 7 (7.000000 unrounded), midsegment 12. |
| Base b from area 50, base a 8, height 5 | same model | Base b 12 (12.000000 unrounded), midsegment 10. |
| Base b from area 96, base a 10, height 8 | same model | Base b 14 (14.000000 unrounded), midsegment 12. |
| Parallelogram: bases 10 and 10, height 6 | same model | Area 60 square units (60.000000 unrounded), midsegment 10. |
| Triangle: base b 0, base a 10, height 6 | same model | Area 30 square units (30.000000 unrounded), midsegment 5. |
| Bases 20 and 30, height 10 | same model | Area 250 square units (250.000000 unrounded), midsegment 25. |
| Base a 0 | same model | Base a — more than 0.. |
| Height −5 | same model | Height — more than 0.. |
| Height mode, both bases 0 | same model | The two bases must add to more than 0.. |
| Base mode, solved base negative (area 50, a 30, h 5) | same model | No such trapezoid — the solved base is negative.. |
| Base b −2 | same model | Base b — 0 or more.. |
| Very large: bases 1,000,000 and 2,000,000, height 3,000,000 | same model | Area 4500000000000 square units (4500000000000.000000 unrounded), midsegment 1500000. |
| Decimals: bases 3.25 and 4.75, height 2.5 | same model | Area 10 square units (10.000000 unrounded), midsegment 4. |
| Height mode: area 100, bases 10 and 10 | same model | Height 10 (10.000000 unrounded), midsegment 10. |
| Base mode: area 200, base a 15, height 10 | same model | Base b 25 (25.000000 unrounded), midsegment 20. |
| Parallelogram: bases 5 and 5, height 4 | same model | Area 20 square units (20.000000 unrounded), midsegment 5. |
| Midsegment check: bases 8 and 12 | same model | Area 50 square units (50.000000 unrounded), midsegment 10. |
The calculator is exact arithmetic on the numbers you type: (8 + 12) / 2 × 5 is exactly 50, and the midsegment is exactly 10. Decimals work the same way — 7.5 and 12.5 average to exactly 10. What it cannot do is measure your trapezoid for you: if the bases you type are not the parallel sides, or the height you type is a slanted leg instead of the perpendicular distance, the answer is the area of a different shape. It also cannot find a height from the legs alone — a height needs a right angle, a right triangle, or the area and the two bases. Base b may be 0, which is a triangle; a solved base below zero means no such trapezoid exists, and the calculator says so.
With bases 8 and 12 and a height of 5, the trapezoid’s area is 50 square units — the average of the bases is 10, times the height of 5. Bases 10 and 6, height 4: area 32. Bases 7.5 and 12.5, height 6: area 60. Smallest whole height for area 50 or more (bases 8 and 12): 5. Smallest whole base b for area 50 or more (base a 8, height 5): 12. Largest whole base a for area 60 or less (base b 12, height 6): 8. Smallest whole height for area 100 or more (bases 10 and 20): 7. Largest whole height for area 50 or less (bases 8 and 12): 5. Smallest whole height for area 60 or more (bases 7.5 and 12.5): 6. Source: Bright Side Kit, brightoolbox.com.
Add the two bases, divide by 2, and multiply by the height: (8 + 12) / 2 × 5 is 50 square units. The two bases are the parallel sides, and the height is the perpendicular distance between them.
The midsegment is the average of the two bases — (8 + 12) / 2 is 10 here. It is the segment joining the midpoints of the two legs, and its length is the average base, so the area is just the midsegment times the height.
Height is twice the area divided by the sum of the bases: 2 × 50 / (8 + 12) is 5. Switch the calculator to Height mode and it does the rearrangement for you.
Base b is twice the area divided by the height, minus base a: 2 × 50 / 5 − 8 is 12. Switch the calculator to Base b mode and it does the rearrangement for you.
The trapezoid becomes a parallelogram, and the formula still works: bases 10 and 10 with height 6 give an area of 60. The average of two equal numbers is the number itself, so the area is just base times height.
The trapezoid becomes a triangle: base b 0, base a 10, height 6 give an area of 30. The formula gives half of base times height, which is exactly the triangle area formula.
No — the height is the perpendicular distance between the bases, and a slanted leg is always at least as long. Using a leg as the height overstates the area; measure straight across, at a right angle to the bases.
No — a solved base below zero means no such trapezoid exists, and the calculator says so. The area is too small for the base and height you gave it: check the numbers and try again.