Midline is the average
The segment through the legs’ midpoints is parallel to the bases and exactly (a+b)/2 long—no extra geometry needed.
Built-in mean
Trapezoid Calculator — Bases, Legs, Height, Area, Perimeter
Diagram & Inputs
Tip: Use bases a (bottom) and b (top) with any of h, A, P, c, or d. Toggle Isosceles or Right when appropriate to unlock more solutions.
Results
How the Trapezoid Calculator Works
A trapezoid (US) or trapezium (UK) is a quadrilateral with one pair of parallel sides, called the bases a (bottom) and b (top). Its height h is the perpendicular distance between the bases, while the non-parallel sides are the legs c (left) and d (right). From these, key measures follow: area A = h(a + b)/2, perimeter P = a + b + c + d, and the midline (average base) m = (a + b)/2 which equals the average of the two bases and has the same length as the segment joining the midpoints of the legs.
Because a trapezoid has two independent base lengths and a perpendicular height, many input combinations are valid. If you know the bases and height, you immediately get the area. If you know the bases and the legs, you can recover the height using horizontal projections of the legs. Let s = a − b (take sign from the drawing). Solving the pair of right triangles along the legs gives the horizontal foot position x = ( (c² − d²) + s² ) / (2s) and then h = √(c² − x²). In the isosceles trapezoid (legs equal), the overhangs balance: c = d = L = √( h² + (s/2)² ), and the two diagonals are equal with length √(h² + ((a + b)/2)²). In a right trapezoid, one leg equals the height and the other leg satisfies L = √(h² + s²).
This tool tries to infer a consistent set of dimensions from your inputs, warns if extra values disagree within a small tolerance, and still shows a best-fit set for learning. All computation runs locally in your browser for privacy and speed. Choose units (areas auto-label with squared units) and control rounding with the decimal-places setting.
Understanding Trapezoids (Examples & Illustrations)
A trapezoid (US) / trapezium (UK) has one pair of parallel sides: the bases a (bottom) and b (top). The height h is the perpendicular distance between the bases; the non-parallel sides are the legs c (left) and d (right). Three core relationships connect all common measures:
- Area:
A = h(a + b)/2(average base × height) - Perimeter:
P = a + b + c + d - Midline:
m = (a + b)/2(a segment parallel to the bases through the legs’ midpoints)
With these, many input pairs determine the entire shape. For example, knowing a, b, and h yields the area immediately. With a, b, c, and d, you can recover the height using right-triangle projections along the legs. In the isosceles case (c = d), symmetry gives clean formulas for legs and diagonals. A right trapezoid has one leg perpendicular to the bases, which simplifies solving. The mini-figures below show these ideas at a glance.
Area = Average Base × Height
Think of the area as the rectangle with width equal to the average of the two bases and height h.
Isosceles Trapezoid (c = d)
Equal legs force equal overhangs, giving tidy expressions for the leg length and equal diagonals.
Right Trapezoid
One leg equals the height. The other leg follows a Pythagorean relation using the base difference.
Height from a, b, c, d
Project each leg horizontally. The difference of projections equals a − b; solve for the foot position x and then the height.
Midline Intuition
The midline equals the average base and “acts like” the width of an equivalent rectangle of height h.
Common input sets and how the solver proceeds:
(a, b, h) ⟶ A = h(a+b)/2, then P if legs are known;
(a, b, c, d) ⟶ recover h via projections, then A and P;
Isosceles with (a, b, h) ⟶ L, equal diagonals, and P;
Right with (a, b, h) ⟶ one leg equals h, the other is √(h² + (a−b)²).
Everything runs client-side for privacy; lengths use your chosen unit, and areas auto-label with squared units.
5 Fun Facts about Trapezoids
Isosceles goes cyclic
An isosceles trapezoid is always cyclic, so its diagonals match. It shares that “equal diagonals” perk with rectangles and squares.
Circle-friendly
Area = average base × height
Unlike triangles, you don’t need an angle: the area is just the mean of the bases multiplied by height—think “average width” times height.
Area intuition
Right leg = height shortcut
In a right trapezoid, one leg is literally the height. The other leg is a single Pythagoras away: √(h² + (a−b)²).
Quick solve
Shape on a spectrum
Let the bases match (a=b) and you get a parallelogram; shrink one base toward zero and it morphs into a triangle. Trapezoids sit between both worlds.
Between shapes