How this instrument works
The midsegment of a trapezoid, sometimes called the median, is the segment joining the midpoints of the two non-parallel sides, the legs. It equals the plain arithmetic average of the two parallel bases, m = (b₁ + b₂) ⁄ 2, and it always runs parallel to both of them. One clean way to see why: draw a diagonal to split the trapezoid into two triangles that share it, and the midsegment splits along with it into two pieces, each a triangle midsegment for its own triangle — those two halves add up to half of b₁ plus half of b₂.
A useful edge case shows the formula's reach. Shrink Base 2 down to a single point and the trapezoid collapses into a triangle; the same formula then reads m = (b₁ + 0) ⁄ 2 = b₁ ⁄ 2 — precisely the triangle midsegment theorem found elsewhere on this site, applied to the triangle's third side. The trapezoid identity is the general case, and the triangle one is simply what remains once a trapezoid loses one of its parallel sides.
This page assumes only the two bases are already known, the narrowest starting point among the trapezoid tools here. The combined trapezoid calculator instead takes all five measurements, both bases, both legs, and the height, and reports area and perimeter together; trapezoid-height solves for the vertical gap between the bases; trapezoid-perimeter simply sums all four sides. Each one answers a different question from a different set of knowns, not the same question asked twice.
- Enter the length of Base 1, one of the trapezoid's two parallel sides.
- Enter the length of Base 2, the other parallel side — order doesn't matter, since the formula treats both the same way.
- Read Midsegment length: the segment joining the midpoints of the two legs, always parallel to both bases.
- Keep both bases in the same length unit; the midsegment comes back in that same unit.
Worked example — bases of 6 and 10
A trapezoidal deck has parallel edges of Base 1 = 6 m at the front rail and Base 2 = 10 m at the back rail. The midsegment is the average of the two: m = (6 + 10) ⁄ 2 = 16 ⁄ 2 = 8 m exactly, the length of a single support beam that would run parallel to both rails through the midpoints of the two slanted side rails.
Notice the height and the leg lengths never entered the calculation. That 8 m answer holds whether the deck is tall and narrow or short and wide, because the midsegment depends only on how far apart the two parallel edges measure, not on the shape of whatever connects them.
Questions
What is the midsegment of a trapezoid?
It's the segment connecting the midpoints of a trapezoid's two legs, the non-parallel sides, and its length is always the average of the two bases: m = (b₁ + b₂) ⁄ 2. It also runs parallel to both bases, sitting exactly halfway between them.
How is the trapezoid midsegment formula derived?
Draw either diagonal to split the trapezoid into two triangles that share it. The midsegment crosses both triangles, and in each one it acts as a triangle midsegment, half of one base, because it joins two midpoints. Adding those two halves gives (b₁ + b₂) ⁄ 2 for the whole segment.
How does this relate to the triangle midsegment theorem?
They are the same statement at different scales. Let one base shrink to a point and the trapezoid becomes a triangle; the formula (b₁ + b₂) ⁄ 2 reduces to b₁ ⁄ 2 once b₂ = 0, which is exactly the triangle midsegment theorem: a segment joining two midpoints is half the remaining side.
Does the midsegment depend on the height or the leg lengths?
No. Only the two base lengths matter — m = (b₁ + b₂) ⁄ 2 has no height or leg term in it at all. Two trapezoids with identical bases but very different heights or slanted legs share the exact same midsegment length.
What's a common mistake with this formula?
Adding the two bases and forgetting to divide by two, which doubles the true answer, or dividing only one base by two and adding the other whole. Either error is easy to catch, because the midsegment must always land strictly between the shorter base and the longer one.
Which measurements does this calculator need?
Just the two base lengths, Base 1 and Base 2. It needs no height, no leg lengths, and no angle, unlike the combined trapezoid calculator on this site, which solves for area and perimeter from all five measurements at once.