Calculate the midsegment (median) of a trapezoid from two parallel sides, or from area and height. Shows midsegment visualization, area, perimeter, height, and reference table.
The midsegment (also called the median or midline) of a trapezoid is the segment connecting the midpoints of the two non-parallel sides (legs). Its length is simply the arithmetic mean of the two parallel bases: m = (a + b) / 2. This elegant property makes it one of the most useful measures for quick calculations involving trapezoids.
The midsegment theorem for trapezoids states that the midsegment is parallel to both bases and its length equals their average. A powerful consequence is that the area of a trapezoid can be expressed as A = m × h, where h is the height. This means the midsegment plays the same role as the "effective base" of a rectangle with the same height and area.
In practical applications the midsegment appears in land surveying (calculating the area of trapezoidal plots by measuring the midline), architecture (roof truss design), and road engineering (cross-sections of embankments). If you know the area and height but not the individual bases, the midsegment is found instantly as m = A / h, and conversely, knowing m and h gives the area.
This calculator offers three input modes: from two bases directly, from area and height, and a full-detail mode including legs. It outputs the midsegment, area, height, perimeter, and a rich visual comparison of the bases and midline.
The midsegment is one of the fastest ways to understand a trapezoid because it compresses the two bases into a single average length. Once you know that median, area becomes midsegment times height and many comparison questions become much easier to reason about. This calculator is useful for geometry proofs, trapezoidal cross-sections in surveying, and any problem where you need to move back and forth between bases, area, and height.
Midsegment: m = (a + b) / 2 From area & height: m = A / h Area: A = m × h = ½(a + b) × h Perimeter: P = a + b + leg₁ + leg₂
Result: Midsegment = 8 units
In bases mode, the median is the average of the two parallel sides. With topBase = 6 and bottomBase = 10, m = (6 + 10) / 2 = 8. That means the segment joining the leg midpoints is 8 units long and parallel to both bases.
The trapezoid midsegment connects the midpoints of the two non-parallel sides, and that placement forces it to run parallel to both bases. Its length becomes the arithmetic mean of the two bases, which is why it behaves like an effective base for the whole figure. This average is often easier to work with than carrying both base lengths through every step of a solution.
Because trapezoid area can be written as area = midsegment x height, the median is also the cleanest bridge between area and altitude. If a survey sketch gives cross-sectional area and fill depth, the midsegment can be recovered immediately as A / h. If the bases are known, the same value checks whether the area output is reasonable for the chosen height.
A midsegment much closer to the longer base than the shorter one usually signals a wide flare between the legs, while a value close to both bases suggests a near-parallelogram. In classroom geometry, it is also a convenient proof target because it ties together parallel lines, averages, and area in one statement. That makes the midsegment a summary measurement, not just another segment length.
It is the segment connecting the midpoints of the two legs. Its length equals the average of the two parallel bases: m = (a + b) / 2.
Yes. "Midsegment," "median," and "midline" are all names for the same segment in a trapezoid.
Area = midsegment × height. The midsegment acts like the effective base of an equivalent rectangle with the same height.
Yes: m = A / h. This is the inverse of the area formula.
Yes. The midsegment theorem guarantees it is parallel to both bases.
The midsegment equals both bases, and the trapezoid is actually a parallelogram (or rectangle, if the angles are 90°). Use this as a practical reminder before finalizing the result.