Trapezoid Area Calculator
Calculate the area of any trapezoid by entering its two parallel bases and height. Useful for land surveying, architecture, and geometry problems involving quadrilaterals with one pair of parallel sides.
About this calculator
A trapezoid (also called a trapezium outside North America) is a four-sided polygon with exactly one pair of parallel sides, called the bases. Its area is found by averaging the two bases and multiplying by the perpendicular height: Area = ½ × (base₁ + base₂) × height. Geometrically, this formula works because a trapezoid can be seen as the average of two rectangles — one with width base₁ and one with width base₂ — each sharing the same height. The height must be the perpendicular distance between the two bases, not the length of the slanted leg. This formula is widely applied in civil engineering when computing cross-sectional areas of channels, roads, and retaining walls.
How to use
Imagine a garden bed shaped like a trapezoid. The shorter parallel side (Base 1) is 4 m, the longer parallel side (Base 2) is 10 m, and the perpendicular height between them is 5 m. Apply the formula: Area = 0.5 × (4 + 10) × 5 = 0.5 × 14 × 5 = 35 m². Enter 4 in the Base 1 field, 10 in Base 2, and 5 in Height. The calculator instantly returns 35 square units, telling you exactly how much soil or mulch you need to fill the bed.
Frequently asked questions
What is the difference between the height and the slant side of a trapezoid?
The height is the perpendicular distance between the two parallel bases — it forms a 90° angle with both bases. The slant side (or leg) is the actual angled edge connecting the two bases, and it is always longer than the height unless the trapezoid is a rectangle. Only the perpendicular height enters the area formula. If you measure the slant side by mistake, your area calculation will be too large, so always confirm you are using the true vertical distance.
How do I find the area of a trapezoid if I only know the side lengths?
If you know all four side lengths but not the height, you can calculate the height using the Pythagorean Theorem on the right triangle formed when you drop a perpendicular from one corner of the shorter base to the longer base. Specifically, if the difference in base lengths is d = base₂ − base₁ and the leg length is l, the height is h = √(l² − (d/2)²) for an isosceles trapezoid. For a non-isosceles trapezoid the geometry is slightly more involved. Once height is known, plug it into Area = ½ × (base₁ + base₂) × h.
Why does the trapezoid area formula average the two bases?
Averaging the bases gives the length of the trapezoid's median — an imaginary line running parallel to the bases, exactly halfway between them. A rectangle with that median length and the same height would have exactly the same area as the trapezoid. This equivalence is why the formula works: you are essentially finding the area of an equivalent rectangle. The approach generalises neatly from the rectangle area formula (length × width) by substituting the average base for length.