Trapezoid Perimeter Calculator
Enter the four sides of a trapezoid to get its perimeter instantly. You can also leave one leg blank and supply the height or a base angle instead, and the calculator will work out the missing side using trigonometry. Choose the trapezoid mode that matches your shape: general, isosceles (equal legs), or right trapezoid (one vertical leg). Switch between metric and imperial units at any time.
What is the perimeter of a trapezoid?
The perimeter of a trapezoid is the total length around its boundary: the sum of its two parallel sides (called bases) and its two non-parallel sides (called legs). If the bases are a and b and the legs are c and d, the formula is simply P = a + b + c + d. Because it is a direct sum of four measurements, the perimeter calculation itself is always straightforward once you know all four sides.
Trapezoid types and which formula to use
A general trapezoid has four sides of any length. An isosceles trapezoid has equal legs (c = d), so the formula simplifies to P = a + b + 2c and also lets you derive the height with the Pythagorean theorem. A right trapezoid has one leg perpendicular to the bases, so that leg equals the height. When you know a leg and the base angle at it, you can use trigonometry to find the other leg: height h = c x sin(alpha) and then d = h / sin(beta). This calculator handles all four scenarios.
How height and area relate to perimeter
Perimeter and area are independent properties: two trapezoids with the same perimeter can have very different areas, and vice versa. For the three modes that provide height information (isosceles, right, or angle input), this calculator also shows the area using the formula A = ((a + b) / 2) x h, which equals the average base times the height. The median (or mid-segment) of a trapezoid is the segment joining the midpoints of the two legs; its length is always (a + b) / 2, exactly the average of the bases.
Practical applications of trapezoid perimeter
Trapezoid perimeters appear in architecture (trapezoidal windows, rooflines, and concrete forms), land surveying (irregularly shaped plots that are sometimes approximated as trapezoids), graphic design (cropped or angled panels), and engineering (cross-sections of channels or retaining walls). Knowing the perimeter tells you how much framing, edging, or border material you need; knowing the area tells you how much surface to cover.
Common trapezoid types and their perimeter formulas
| Type | Known sides | Perimeter formula |
|---|---|---|
| General trapezoid | a, b, c, d | P = a + b + c + d |
| Isosceles trapezoid | a, b, c (= d) | P = a + b + 2c |
| Right trapezoid | a, b, h (= c), d | P = a + b + h + d |
| Parallelogram (special) | a (= b), c (= d) | P = 2(a + c) |
| Rectangle (special) | a (= b), h (= c = d) | P = 2(a + h) |
Each trapezoid type simplifies the full P = a + b + c + d formula depending on which sides are equal or right-angled.
Frequently asked questions
What is the formula for the perimeter of a trapezoid?
The perimeter of a trapezoid equals the sum of all four sides: P = a + b + c + d, where a and b are the two parallel bases and c and d are the two legs. For an isosceles trapezoid (equal legs) this simplifies to P = a + b + 2c.
How do I find the perimeter if I only know two sides and an angle?
If you know both bases, one leg (c), and the base angle at that leg (alpha), you can find the height with h = c x sin(alpha) and then use the base angle at the other leg (beta) to derive the unknown leg d = h / sin(beta). You can then compute P = a + b + c + d. Select "From bases, one leg and a base angle" in this calculator to do this automatically.
What is an isosceles trapezoid?
An isosceles trapezoid has two equal legs (non-parallel sides). Its two base angles are also equal, and the diagonals are equal in length. The symmetry lets you compute the height from just the bases and one leg: h = sqrt(c^2 - ((a - b) / 2)^2).
What is a right trapezoid?
A right trapezoid has exactly two right angles, both at the same leg. That vertical leg equals the perpendicular height between the bases. The perimeter is P = a + b + h + d, where h is the vertical leg and d is the oblique leg.
What is the median of a trapezoid?
The median (or mid-segment) is the line segment connecting the midpoints of the two legs. Its length is always the arithmetic mean of the two bases: M = (a + b) / 2. The area of the trapezoid equals the median times the height: A = M x h.
Can the perimeter be the same for different trapezoid shapes?
Yes. Two trapezoids with the same perimeter can have completely different areas and angles. Perimeter measures total boundary length, while area depends on how the enclosed space is distributed. A very "flat" trapezoid and a taller one can share the same perimeter while looking quite different.