How this instrument works
An isosceles trapezoid carries two equal, non-parallel legs alongside its two parallel bases, and its perimeter is nothing more than the sum of all four boundary lengths: the two bases plus both legs. Because the legs match, that sum simplifies to base1 + base2 + 2×leg, needing only three figures rather than four — enter both bases and a single leg length, and this sheet doubles that leg and adds it to the two bases in one step.
A sibling page already live on this site takes the identical three measurements — both bases and one equal leg — and instead works out the height and the enclosed area, deriving that hidden height through the Pythagorean theorem before it can report a square-unit figure. This page skips all of that. Perimeter never needed the height in the first place, so there is no derivation step here at all, just a direct sum of the four sides.
That narrowness is deliberate rather than a missing feature. Plenty of real questions genuinely stop at how much edging, fencing, or trim a shape needs, and for those, running a square-root derivation just to throw the height away afterward wastes a step. This page exists for exactly that shorter path — three numbers in, one sum out, nothing about area touched at all.
- Enter the first parallel length into Base 1.
- Enter the second parallel length into Base 2.
- Enter the length shared by both non-parallel sides into Leg (both equal legs).
- Read Perimeter: the two bases plus twice the leg, added in one step.
Worked example — bases 6 and 10, a leg of 5
An isosceles trapezoid has bases of 6 and 10, with both slanted legs measuring 5 apiece. Perimeter adds all four: P = 6 + 10 + 2×5 = 6 + 10 + 10 = 26 — no height, no square root, just the four boundary lengths summed directly.
Shrink the shorter base to 0 and the shape collapses into a plain triangle with two 5-unit sides and one 10-unit base; the same formula still works, giving P = 0 + 10 + 2×5 = 20. Widen the shorter base instead until both bases read 8, and the shape becomes a parallelogram-like figure with P = 8 + 8 + 2×5 = 26 — matching the first case exactly, since perimeter only tracks the four lengths and never checks the angles between them.
Questions
What is the formula for an isosceles trapezoid's perimeter?
P = b1 + b2 + 2×leg — add the two parallel bases to twice the single equal-leg length. Bases of 6 and 10 with a leg of 5 give P = 6 + 10 + 10 = 26, a plain sum with no square root or angle involved anywhere.
Why does this page only ask for one leg instead of two?
Because an isosceles trapezoid's two non-parallel sides share one length by definition, so a single Leg field already describes both of them. Doubling that one figure and adding it to the two bases gives the full four-sided total without asking for redundant information.
How is this different from the isosceles trapezoid area page on this site?
That page takes the same three inputs — both bases and one leg — but derives the height first, using the Pythagorean theorem, before reporting an area in square units. This page needs no height at all, since a perimeter is just a sum of lengths, so it skips that derivation entirely and returns one figure directly.
What happens if I set both bases to the same length?
The trapezoid becomes a rhombus-like parallelogram, and the perimeter formula still applies without change: two equal bases of 8 plus two legs of 5 give P = 8 + 8 + 10 = 26, the same total four boundary lengths always add to, regardless of the shape's angles.
What if the shorter base shrinks to zero?
The shape becomes an isosceles triangle, and the formula still holds: a shorter base of 0, a longer base of 10, and legs of 5 apiece give P = 0 + 10 + 10 = 20, correctly dropping the zero-length side while still summing the remaining three.
Do I need to know the trapezoid's height to use this page?
No — perimeter never involves height at all, only the four boundary lengths. That is exactly what separates this page from the area version of the same three inputs, which cannot skip the height, since area measures enclosed surface rather than boundary length.