No personal result is available. These are the trapezoid formulas and conditions.
Formulas and conditions
Trapezoid
Area
Perimeter
b₁, b₂ parallel bases · c, e legs · h perpendicular height · A area · P perimeter
Positive lengths and parallel bases. Equal bases are included as a parallelogram case.
Use h, not a sloping leg. Perimeter needs all four sides.
Diagrams are schematic, not to scale.
Bases and height gives area from the average of the two parallel bases times their perpendicular distance. It does not determine the legs or perimeter.
For Four sides with unequal bases, let D = |b₁ − b₂|. A positive height exists only when |c − e| < D < c + e. The auxiliary triangle with sides D, c and e has area T; its height is also the trapezoid height. Overhanging legs are allowed.
With equal bases and equal legs, perimeter is known but height and area are not unique. Height is needed to find area: choose Bases and height. Equal bases with unequal legs cannot make this convex shape.
Height from auxiliary triangle
Use the same length unit throughout a formula. Convert mixed measurements first. Length and perimeter use units such as cm; area uses cm²; volume uses cm³. Decimal examples below are rounded to at most six significant figures, with ≈ marking an approximation.
Worked example: Bases 20 cm and 6 cm; legs 13 cm and 15 cm
D = 20 − 6 = 14 cm. The auxiliary triangle has sides 14, 13 and 15 cm.
Its half perimeter is 21 cm, so T = √(21 × 7 × 8 × 6) = 84 cm².
h = 2 × 84 ÷ 14 = 12 cm.
A = (20 + 6) × 12 ÷ 2 = 156 cm²; P = 20 + 6 + 13 + 15 = 54 cm.
At height 12 cm, the legs have horizontal offsets 5 cm and 9 cm by the 5–12–13 and 9–12–15 right triangles. Their sum is the 14 cm base difference. A sloping leg is not the height.