Right Trapezoid Profile

CREATE 2D PROFILE ON XY PLANE UNITS: millimeters GEOMETRY TYPE: right trapezoid COORDINATE SYSTEM: XY Cartesian coordinate system Origin = (0,0) VERTICES: D = (0,0) A = (42,0) C = (0,820) B = (68,820) CONNECT VERTICES IN THIS ORDER: A → B → C → D → A SIDES: AB = line segment from A to B BC = line segment from B to C CD = line segment from C to D DA = line segment from D to A SIDE DIMENSIONS: DA = 42 mm BC = 68 mm CD = 820 mm AB = DERIVED DIMENSION GEOMETRIC CONSTRAINTS: DA ∥ BC CD ⟂ DA CD ⟂ BC Angle D = 90° Angle C = 90° ORIENTATION: DA lies on the positive X-axis. D is the origin. CD lies on the positive Y-axis. A lies at X = 42 mm, Y = 0 mm. C lies at X = 0 mm, Y = 820 mm. B lies at X = 68 mm, Y = 820 mm. DERIVED GEOMETRY: Horizontal offset between A and B = 68 − 42 = 26 mm. Vertical offset between A and B = 820 mm. CALCULATE SIDE AB: AB = sqrt((68 − 42)^2 + 820^2) AB = sqrt(26^2 + 820^2) AB = sqrt(676 + 672400) AB = sqrt(673076) AB ≈ 820.412 mm DIMENSIONAL REQUIREMENT: Set or report AB = 820.412 mm. Do not independently modify AB. AB must be determined by the specified vertex coordinates and geometric constraints. VERTEX LABELS: A = upper-right relative to the XY-axis orientation B = upper-rightmost C = upper-left D = origin / lower-left ANGLE LABELS: Angle A = interior angle at vertex A Angle B = interior angle at vertex B Angle C = 90° Angle D = 90° FINAL VALIDATION: Verify that: 1. DA = 42 mm. 2. BC = 68 mm. 3. CD = 820 mm. 4. AB ≈ 820.412 mm. 5. DA is parallel to BC. 6. CD is perpendicular to DA. 7. CD is perpendicular to BC. 8. C and D are exactly 90° interior angles. 9. D = (0,0). 10. The resulting profile is a single closed four-sided right trapezoid. 11. No additional geometry is created.

Parameters

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