Trapezoid Calculator
Calculate the area and perimeter of a trapezoid using its two parallel bases, height, and optional leg lengths. Commonly used in construction, land surveying, and geometry coursework.
About this calculator
A trapezoid (or trapezium) is a quadrilateral with exactly one pair of parallel sides, called the bases (b₁ and b₂). Its area is found by averaging the two bases and multiplying by the perpendicular height h: A = ((b₁ + b₂) × h) / 2. This formula works because a trapezoid can be thought of as a rectangle with two triangles added or removed at the sides. The perimeter is P = b₁ + b₂ + leg₁ + leg₂, where the legs are the two non-parallel sides. If the legs are not given, only the area can be computed. The height must be perpendicular to both bases — not the slant length of a leg — for the area formula to apply correctly.
How to use
Suppose a trapezoid has a top base (b₁) of 6 units, a bottom base (b₂) of 10 units, a height of 4 units, and legs of 5 and 5 units. The area is A = ((6 + 10) × 4) / 2 = (16 × 4) / 2 = 64 / 2 = 32 square units. The perimeter is P = 6 + 10 + 5 + 5 = 26 units. Enter these values into the corresponding fields — Base 1 = 6, Base 2 = 10, Height = 4, Left Leg = 5, Right Leg = 5 — and the calculator returns both results instantly.
Frequently asked questions
How do you calculate the area of a trapezoid without knowing the leg lengths?
The area formula A = ((b₁ + b₂) × h) / 2 requires only the two parallel bases and the perpendicular height — leg lengths are not needed. For example, a trapezoid with b₁ = 5, b₂ = 9, and h = 3 has area = ((5 + 9) × 3) / 2 = 21 square units. The legs affect only the perimeter. If you know the height but not the legs, you can still compute the area precisely.
What is the difference between the height and the leg of a trapezoid?
The height of a trapezoid is the perpendicular distance between the two parallel bases, measured at a right angle. A leg is the actual slant length of one of the non-parallel sides. These are equal only in a right trapezoid where one leg is vertical. Confusing slant length with perpendicular height is a common error that overstates the area. Always use the vertical height — not the leg length — in the area formula A = ((b₁ + b₂) × h) / 2.
When would a trapezoid shape appear in real-world construction or surveying?
Trapezoidal cross-sections are common in irrigation channels, road embankments, and retaining walls, where one face is wider than the other for structural stability. Land parcels bounded by two parallel roads but narrowing at one end are modelled as trapezoids for area calculations. Roof sections and staircase stringers also frequently form trapezoidal shapes. Accurate area calculation determines material volumes — concrete, soil, or water — needed for these projects.