How this instrument works
This sheet takes all five trapezoid measurements at once — both parallel bases, the height between them, and both slanted legs — and returns area and perimeter together. That is a deliberate choice: most practical trapezoid questions, a deck footprint, a garden bed, a cut panel, need both numbers in the same breath, one for how much surface a material has to cover and one for how much boundary needs trimming or fencing. A page that solves only the area from two bases and a height answers half of that question; this one answers both from what you have already measured.
There is a reason the height still gets its own field even though the two bases and two legs are already on the page. For a trapezoid with unequal bases, those four side lengths algebraically pin the height to one specific value — work the shape out in coordinates and only one height fits, up to flipping the figure over, much the way three side lengths pin a triangle's shape and no other. Almost nobody wants to run that algebra by hand, so this instrument accepts a height measured directly instead of one that would otherwise have to be derived.
Push the two bases to equal lengths and the shape becomes a parallelogram, and the rule above breaks down on purpose: a parallelogram's height is no longer fixed by its four sides, it can lean over like an unbraced gate while every side keeps its length. Shrink one base to zero instead and the trapezoid collapses into a plain triangle, and both formulas still return the right numbers without any special-casing. Neither edge case needs to be told apart from the general case — the same two formulas already cover them.
- Enter the two parallel side lengths into Base 1 and Base 2 — the formulas treat them symmetrically, so either order works.
- Enter the perpendicular distance between the two bases into Height, not the length of a slanted side.
- Enter the two slanted side lengths into Leg 1 and Leg 2.
- Read Area for the enclosed surface and Perimeter for the total boundary length; both are computed together from all five entries.
Worked example — a 6 m and 10 m deck footprint
A trapezoidal deck extension has parallel edges of 6 m and 10 m, a perpendicular height of 4 m between them, and two 5 m rails closing the sides. Area: A = ½(6 + 10) × 4 = ½ × 16 × 4 = 32 m² — the figure a decking supplier needs to know how many boards to cut. Perimeter: P = 6 + 10 + 5 + 5 = 26 m — the total run of edge trim or railing needed around the whole boundary.
Both numbers come from the same five measurements in one pass, which is the entire point of a calculator that accepts all five rather than asking you to derive one of them from the others first. A tape measure gives every one of Base 1, Base 2, Height, Leg 1, and Leg 2 directly on site, without needing to solve for a hidden length algebraically before the arithmetic can even start.
Questions
What is the formula for a trapezoid's area and perimeter?
Area is A = ½(b₁ + b₂)h, the average of the two parallel bases times the height between them. Perimeter is simply P = b₁ + b₂ + leg₁ + leg₂, the plain sum of all four sides. With bases 6 and 10, height 4, and legs of 5 apiece, that gives A = 32 and P = 26.
Why does this calculator ask for height separately from the two legs?
Because a trapezoid with unequal bases is close to rigid: once the two base lengths and two leg lengths are fixed, straightforward algebra pins the height to one specific value, the way three side lengths pin a triangle's shape. Few people want to solve that system by hand, so this sheet takes a directly measured height instead and runs both formulas from all five numbers as given.
What happens when one base is zero?
The trapezoid degenerates into a triangle, and both formulas still hold without modification: inputs of 0, 10, 4, 5, and 5 give A = ½(0 + 10) × 4 = 20 and P = 0 + 10 + 5 + 5 = 20, dropping the zero-length side from the sum automatically. It is a useful sanity check that the same two formulas already contain the triangle rules as a special case.
What happens when the two bases are equal?
The shape becomes a parallelogram, and unlike a trapezoid with unequal bases, a parallelogram's height is not pinned by its four side lengths — it can shear like an unbraced gate while every side stays the same length. With bases of 6 and legs of 5 apiece, height 4 gives A = 24 and P = 22, but a different height would give a different area from the same four side lengths, which is exactly why height still needs its own field.
How is this different from a calculator that only takes two bases and a height?
That narrower version answers one question, area, from three measurements. This one answers two questions, area and perimeter, from five, which suits a situation where every side and the height have already been measured directly, such as a deck, a garden bed, or a cut piece of material, with no algebra needed first.
Do the two legs need to be equal for these formulas to work?
No — Leg 1 and Leg 2 can differ freely; nothing about either formula assumes an isosceles trapezoid. Area only ever depends on the two bases and the height, and perimeter is just the sum of whichever four side lengths are entered, symmetric or not.