Trapezoid
Find the area, height, midsegment, perimeter and angles of a trapezoid from the bases and height, all four sides, or for an isosceles trapezoid.
The trapezoid calculator finds the area, height, midsegment, perimeter and angles of a trapezoid. A trapezoid can be given by its bases and height, its bases and legs, three sides of an isosceles trapezoid, the midsegment and height, or the diagonals and the angle between them.
Area formulas
| What is known | Formula |
|---|---|
| Bases and height | S = (a + b)/2 · h |
| Midsegment and height | S = m · h |
| Diagonals and the angle between them | S = ½ · d1 · d2 · sin φ |
The midsegment of a trapezoid is parallel to the bases and equals half their sum: m = (a + b)/2.
Height from the four sides
Draw a line through a vertex of the shorter base parallel to a leg. It forms a triangle with sides c, d and |a − b|. Find its area with Heron's formula; the height of this triangle to the side |a − b| equals the height of the trapezoid.
Example 1. a = 12, b = 4, c = d = 5.
Triangle 5, 5, 8: p = 9, S = √(9 · 4 · 4 · 1) = 12, h = 2 · 12 / 8 = 3.
Strapezoid = (12 + 4)/2 · 3 = 24.
Isosceles trapezoid
The legs are equal, the angles at each base are equal, the diagonals are equal. Height: h = √(c² − ((a − b)/2)²).
Example 2. a = 12, b = 6, c = 5.
h = √(25 − 9) = 4, S = (12 + 6)/2 · 4 = 36, P = 12 + 6 + 2 · 5 = 28.
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