BYTETOOLS

Trapezoid Calculator

Solve a trapezoid from its parallel sides plus a height, both legs or both base angles: area, median, legs, all four angles, diagonals and a scale drawing.

18
Area
6
Median
3
Height
19.2111
Perimeter

Full solution

  • Area = (a + b)·h / 2 = 18
  • Median (midsegment) = (a + b)/2 = 6
  • Height h = 3
  • Legs = 3.605551 and 3.605551
  • Base angles at the longer side = 56.309932° and 56.309932°
  • Angles at the shorter side = 123.690068° and 123.690068°
  • Diagonals = 6.708204 and 6.708204
  • Horizontal offsets = 2 on the left, 2 on the right

The area, median and height above hold for any trapezoid with these parallel sides. The legs, angles and diagonals assume an isosceles trapezoid, because two parallel sides and a height do not fix the slant on their own. Switch mode if you know the legs or the base angles.

Drawing

Drawn to scale. The amber line is the height; the green line is the median, always halfway up and equal to the average of the two parallel sides.

What is the Trapezoid Calculator?

The ByteTools Trapezoid Calculator solves the shape from three different starting points. Give it the two parallel sides and a height, the two parallel sides and both legs, or the two parallel sides and both base angles, and it reconstructs the whole quadrilateral by right-triangle decomposition of the horizontal offsets.

  • Three solving modes: from height, from both legs, or from both base angles
  • Area, median, perimeter, both diagonals and all four interior angles
  • Right-triangle decomposition prints the horizontal offset at each end
  • Flags impossible leg lengths and base angles that cannot close the shape
  • Scale drawing with the height and median marked
  • Runs entirely in your browser — nothing is uploaded

How to use the Trapezoid Calculator

  1. 1

    Pick what you know: bases and height, bases and both legs, or bases and both base angles.

  2. 2

    Enter the two parallel sides, then the extra values the mode asks for.

  3. 3

    Read the area, median, height and perimeter in the summary tiles.

  4. 4

    Check the full solution panel for legs, all four angles, diagonals and offsets.

  5. 5

    Use the scale drawing to confirm the shape, then copy the results.

About the Trapezoid Calculator

The ByteTools Trapezoid Calculator solves the shape from three different starting points. Give it the two parallel sides and a height, the two parallel sides and both legs, or the two parallel sides and both base angles, and it reconstructs the whole quadrilateral by right-triangle decomposition of the horizontal offsets.

Results include the area (a + b)h/2, the median (a + b)/2, the height, both legs, all four interior angles, both diagonals, the perimeter and the offsets at each end. A scale drawing shows the trapezoid with the height and the median marked, so you can see that the median always lies halfway up.

Everything is calculated in your browser using JavaScript, so no measurements are uploaded and the tool works offline. When you supply only the bases and a height, the legs and angles are labelled clearly as an isosceles assumption, because those inputs alone do not fix the slant.

Frequently asked questions

What is the formula for the area of a trapezoid?

Average the two parallel sides and multiply by the height: A = (a + b)h/2. Parallel sides of 8 and 4 with a height of 3 give (12 × 3)/2 = 18 square units. The formula holds whether or not the trapezoid is isosceles.

What is the median of a trapezoid?

The median, or midsegment, joins the midpoints of the two legs. Its length is the average of the parallel sides, (a + b)/2, and it always sits exactly halfway up. For bases of 8 and 4 the median is 6, which is why the area is just median times height.

How do you find the height of a trapezoid from its legs?

Split the difference between the parallel sides into two horizontal offsets x and y using x = ((a - b)² + c² - d²)/(2(a - b)), then take h = √(c² - x²). If that square root would be negative, the legs are too short to bridge the gap and no such trapezoid exists.

Can I calculate a trapezoid from only the bases and the height?

You can get the area, the median and the height itself, but not the legs, angles or diagonals — infinitely many trapezoids share those three numbers with different slants. This tool shows those extra values under an explicit isosceles assumption and labels it as such.

Why do my base angles produce an error?

If both base angles at the longer side are 90° or more, the legs never lean inward and can never reach the shorter parallel side, so no trapezoid closes. The tool checks whether cot A + cot B is positive before computing a height.

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