Trapezoid Calculator
Calculate the area, perimeter, height, and diagonal length of any trapezoid from its sides and height.
🔶 What is a Trapezoid?
A trapezoid (called a trapezium in British English) is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases (typically labeled a for the shorter top base and b for the longer bottom base). The non-parallel sides are called legs. The perpendicular distance between the two bases is the height (h).
Trapezoids come in several types. An isosceles trapezoid has equal legs — it is symmetric, with equal base angles and equal diagonals. A right trapezoid has two right angles — one leg is perpendicular to both bases. A general trapezoid has legs of unequal length with no right angles. When both pairs of sides become parallel (legs also become parallel and equal), the trapezoid becomes a parallelogram.
The midsegment (also called the median) of a trapezoid connects the midpoints of the two legs. Its length is the average of the two bases: (a + b) / 2. It is always parallel to the bases, and the area of the trapezoid equals the midsegment times the height — a useful alternative formula.
Trapezoids appear frequently in architecture, civil engineering, and everyday objects: bridge cross-sections, roof trusses, highway lanes narrowing to a merge point, and the cross-section of irrigation channels are all trapezoidal. The area formula is fundamental for land surveying, structural design, and fluid dynamics (cross-sectional flow area in trapezoidal channels).
📐 Trapezoid Formulas
📖 How to Use This Calculator
General Trapezoid
Isosceles Trapezoid
💡 Example Calculations
Example 1 — Standard Trapezoid
a = 8 cm, b = 14 cm, h = 6 cm, legs c = 7 cm, d = 7 cm
Example 2 — Isosceles Trapezoid (Finding Leg from Height)
a = 6 cm, b = 12 cm, h = 4 cm (isosceles)
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for the area of a trapezoid?
Area of a trapezoid = ½ × (sum of parallel sides) × height = (a + b) / 2 × h. Where a and b are the lengths of the two parallel sides (bases), and h is the perpendicular height between them. For example, a trapezoid with parallel sides 8 cm and 12 cm, and height 5 cm: Area = (8 + 12) / 2 × 5 = 10 × 5 = 50 cm².
How do you find the height of a trapezoid?
If you know the area and both parallel sides: h = 2 × Area ÷ (a + b). If you know the leg length and the offset (horizontal distance), use the Pythagorean theorem: h = √(leg² − offset²). For an isosceles trapezoid with bases a and b and leg length l: offset = (a − b) / 2, so h = √(l² − ((a − b) / 2)²).
What is the difference between a trapezoid and a parallelogram?
A trapezoid has exactly one pair of parallel sides. A parallelogram has two pairs of parallel sides (both pairs of opposite sides are parallel and equal). A rectangle, rhombus, and square are all special parallelograms. If the two non-parallel sides (legs) of a trapezoid become parallel and equal, it becomes a parallelogram.
What is an isosceles trapezoid?
An isosceles trapezoid has two legs (non-parallel sides) of equal length. It is symmetric about the perpendicular bisector of the parallel sides. Its diagonals are equal in length, and the base angles are equal. Many real-world shapes are isosceles trapezoids: certain cross-sections of beams, some trays, and architectural arches.
How do you find the perimeter of a trapezoid?
Perimeter = a + b + c + d, where a and b are the parallel sides (bases) and c and d are the two legs (non-parallel sides). If it is an isosceles trapezoid, c = d and perimeter = a + b + 2c. If the leg lengths are not given but height and horizontal offset are known: leg = √(h² + offset²) via Pythagoras.
What is the median (midsegment) of a trapezoid?
The median (or midsegment) of a trapezoid is the segment connecting the midpoints of the two legs. Its length equals the average of the two bases: median = (a + b) / 2. The median is parallel to both bases. The area of the trapezoid can also be written as: Area = median × height.
What is a right trapezoid?
A right trapezoid (or right-angled trapezoid) has exactly two right angles - one leg is perpendicular to both parallel sides, making it the height itself. The other leg is angled. In this case, the perpendicular leg = h (height), and you can use the Pythagorean theorem to find the angled leg: leg = √(h² + (a − b)²), where a and b are the parallel sides. Right trapezoids appear in architectural cross-sections and ramp profiles.
How do you find the diagonals of a trapezoid?
For a general trapezoid with bases a and b, height h, and legs c and d, the diagonals can be found using coordinate geometry. Place the trapezoid in a coordinate system: A=(0,0), B=(a,0), C=(a−offset2, h), D=(offset1, h). Diagonal 1 (A to C) and Diagonal 2 (B to D) can then be computed with the distance formula. For an isosceles trapezoid, both diagonals are equal in length.
What are real-world applications of trapezoids?
Trapezoids appear in: civil engineering (cross-sections of embankments, canals, and road cuttings are trapezoidal); architecture (trapezoidal windows, facades, and roof sections); everyday objects (trapezoidal trays, tables with angled legs, guitar bodies, and some door frames). The trapezoidal rule is also used in calculus to numerically approximate the area under a curve, making trapezoids fundamental in numerical integration.
Is every parallelogram a trapezoid?
It depends on the definition used. In the inclusive definition (used in most modern curricula, including India's NCERT): a trapezoid has 'at least one pair of parallel sides,' so parallelograms (which have two pairs) are a special case of trapezoids. In the exclusive definition (used in some older US curricula): a trapezoid has 'exactly one pair of parallel sides,' excluding parallelograms. This calculator uses the general trapezoid, with no assumption about the legs being parallel.