Trapezoid Calculator

Free Online Trapezoid Calculator

This trapezoid calculator helps you instantly find the area, perimeter, and median (mid-segment) of any trapezoid from its two parallel sides, height, and legs. Just enter the top side, bottom side, height, and both legs, and the calculator instantly computes every measurement, complete with a fully labeled diagram and a step-by-step solution showing exactly how each formula was applied.

Whether you're a student working through geometry and mensuration homework, a teacher preparing worked examples, a land surveyor measuring an irregular plot, or simply someone who needs a fast and accurate area of a trapezoid calculator or perimeter of a trapezoid calculator, this tool covers every common calculation you'll ever need for a trapezoid.

A trapezoid (also called a trapezium in British English) is a four-sided polygon with exactly one pair of parallel sides, known as the bases. The other two sides, called legs, are not parallel to each other. Because a trapezoid can take many different shapes, it needs five measurements — the two bases, the height, and the two legs — to be fully described, which is exactly what this calculator uses to solve everything at once.

Trapezoid Formulas Used

A trapezoid is defined by its two parallel bases (a and b), the perpendicular height (h) between them, and its two legs (c and d). Every measurement below follows from these five values using standard mensuration formulas:

• Area: A = ((a + b) / 2) × h (the average of the two parallel sides, multiplied by the height)
• Perimeter: P = a + b + c + d (the sum of all four sides)
• Median (mid-segment): m = (a + b) / 2 (the segment joining the midpoints of the two legs, always equal to the average of the bases)
• Note: Area can also be written as A = m × h, since the median already represents the average base length

How to Use This Trapezoid Calculator

Using this calculator takes just five quick entries. First, enter the top parallel side (a). Second, enter the bottom parallel side (b). Third, enter the perpendicular height (h) measured straight between the two bases — not along a slanted leg. Fourth and fifth, enter the two legs (c and d). The calculator instantly displays the area, perimeter, and median, along with a labeled diagram where you can see every value marked directly on the shape.

This means you never have to manually apply the trapezoid area or perimeter formula yourself — the calculator handles all the arithmetic instantly. It's especially useful for real-world shapes like sloped roof sections, irregular plots of land, cross-sections of channels or drains, and cake or table designs that taper from a wide base to a narrower top.

Worked Example

Suppose you're calculating the area of a trapezoid-shaped garden bed with a top edge of 6 meters, a bottom edge of 10 meters, and a height of 4 meters between them, with legs of 5 meters on each side. Enter a = 6, b = 10, h = 4, c = 5, and d = 5. The calculator first finds the median (m = (6 + 10) / 2 = 8 meters), then the area (A = 8 × 4 = 32 square meters), and finally the perimeter (P = 6 + 10 + 5 + 5 = 26 meters).

That tells you the garden bed covers 32 square meters of ground and needs 26 meters of edging material to enclose it completely — all calculated instantly from five simple measurements.

Types of Trapezoids

Not all trapezoids look the same. In an isosceles trapezoid, the two legs (c and d) are equal in length and the shape is symmetric, like the one shown in the diagram above. In a right trapezoid, one leg is perpendicular to the bases, forming two right angles on one side. In a scalene trapezoid, both the bases and the legs can all be different lengths, with no symmetry at all. Regardless of the type, the same area and perimeter formulas apply — the only thing that changes is how the legs relate to each other geometrically.

Why the Area Formula Works

The trapezoid area formula, A = ((a + b) / 2) × h, might look like it comes out of nowhere, but it has a simple visual explanation. Imagine taking a second, upside-down copy of the same trapezoid and joining it to the original along one of its legs. The two shapes together form a parallelogram whose base is exactly a + b and whose height is h. The area of that combined parallelogram is base × height, or (a + b) × h — but since it's made of two identical trapezoids, each individual trapezoid must be exactly half of that, giving A = ((a + b) / 2) × h.

This is also why the median (m), the segment joining the midpoints of the two legs, always equals (a + b) / 2 — the average of the two bases. Once you know the median, the area simplifies even further to A = m × h, which is often the fastest way to calculate area if the median is already known or easy to measure directly, such as when working from a scaled drawing or blueprint.

Where Trapezoid Calculations Are Used

Trapezoid geometry and mensuration formulas appear constantly in real life and across many fields of study:

• Students and teachers use it for geometry and mensuration homework, competitive exams, and lesson planning.
• Architects and engineers use trapezoid measurements when designing sloped roofs, retaining walls, bridges, and cross-sections of channels or dams.
• Land surveyors and civil engineers calculate the area of trapezoid-shaped plots of land that don't have four equal or parallel sides.
• Interior designers and carpenters use trapezoid area and perimeter for tapered tabletops, countertops, and custom furniture panels.
• Fashion and textile designers use trapezoid shapes when cutting fabric panels for skirts, tents, and other tapering designs.