{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"parallelogram"},"result":{"entity_type":"calculator","id":"parallelogram","calculator_id":"parallelogram","canonical_url":"https://tttkmbb.com/geometry/parallelogram","name":"Parallelogram Calculator","title":"Parallelogram Calculator – Area from Base and Height, Perimeter, Angles and Diagonals","category":"geometry","category_name":"Geometry","tool_name":"calculate_parallelogram_properties","featured_mcp_tool":false,"description":"Computes the area of a parallelogram from base and height and, when the slanted side is given, its perimeter, the acute angle between base and side in degrees, and both diagonals.","use_when":"You need the area, perimeter, angles or diagonals of a quadrilateral whose opposite sides are parallel (including rhombi).","do_not_use_when":"All angles are right angles (use rectangle) or only one pair of sides is parallel (use trapezoid).","inputs":[{"name":"base","label":"Base","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Length of one side chosen as the base.","example":8},{"name":"height","label":"Height","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Perpendicular distance between the base and its opposite side.","example":5},{"name":"side","label":"Side","type":"number","unit":"units","required":false,"exclusive_min":0,"description":"Length of the slanted side adjacent to the base (optional; must be at least the height).","example":6}],"outputs":[{"name":"area","label":"Area","type":"number","unit":"units²","decimals":4,"description":"base × height."},{"name":"perimeter","label":"Perimeter","type":"number","unit":"units","decimals":4,"description":"2 × (base + side), only when side is given."},{"name":"angle_deg","label":"Acute angle","type":"number","unit":"degrees","decimals":4,"description":"Acute angle between base and side = asin(height / side); the obtuse angle is 180° minus this."},{"name":"diagonal_long","label":"Long diagonal","type":"number","unit":"units","decimals":4,"description":"√(base² + side² + 2·base·√(side² − height²))."},{"name":"diagonal_short","label":"Short diagonal","type":"number","unit":"units","decimals":4,"description":"√(base² + side² − 2·base·√(side² − height²))."}],"input_schema":{"type":"object","properties":{"base":{"description":"Length of one side chosen as the base. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[8],"x-unit":"units"},"height":{"description":"Perpendicular distance between the base and its opposite side. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[5],"x-unit":"units"},"side":{"description":"Length of the slanted side adjacent to the base (optional; must be at least the height). Unit: units.","type":"number","exclusiveMinimum":0,"examples":[6],"x-unit":"units"}},"additionalProperties":false,"required":["base","height"]},"output_schema":{"type":"object","properties":{"area":{"description":"base × height. Unit: units².","type":"number","x-unit":"units²"},"perimeter":{"description":"2 × (base + side), only when side is given. Unit: units.","type":"number","x-unit":"units"},"angle_deg":{"description":"Acute angle between base and side = asin(height / side); the obtuse angle is 180° minus this. Unit: degrees.","type":"number","x-unit":"degrees"},"diagonal_long":{"description":"√(base² + side² + 2·base·√(side² − height²)). Unit: units.","type":"number","x-unit":"units"},"diagonal_short":{"description":"√(base² + side² − 2·base·√(side² − height²)). Unit: units.","type":"number","x-unit":"units"}}},"formula":"area = base × height; perimeter = 2 × (base + side); angle_deg = asin(height / side); diagonals = √(base² + side² ± 2·base·√(side² − height²))","sources":[{"name":"Wikipedia – Parallelogram","url":"https://en.wikipedia.org/wiki/Parallelogram","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wolfram MathWorld – Parallelogram","url":"https://mathworld.wolfram.com/Parallelogram.html","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Base 8, height 5, side 6","inputs":{"base":8,"height":5,"side":6},"expected":{"area":40,"perimeter":28,"angle_deg":56.4427,"diagonal_long":12.372,"diagonal_short":6.8508},"url":"https://tttkmbb.com/api/v1/calculate/parallelogram?base=8&height=5&side=6"},{"name":"Base 10, height 3","inputs":{"base":10,"height":3},"expected":{"area":30},"url":"https://tttkmbb.com/api/v1/calculate/parallelogram?base=10&height=3"}],"faq":[{"q":"Why must the side be at least the height?","a":"The height is the perpendicular distance between the parallel sides, so the slanted side can never be shorter than it; side = height gives a rectangle."},{"q":"How do I compute a rhombus?","a":"Enter side = base. The area is still base × height, or you can use diagonal_long × diagonal_short / 2."}],"tags":["parallelogram","area of a parallelogram","rhombus","diagonals","perimeter"],"related":[{"calculator_id":"rectangle","reason":"Special case with right angles."},{"calculator_id":"trapezoid","reason":"Only one pair of parallel sides."},{"calculator_id":"triangle-area","reason":"Half a parallelogram cut along a diagonal."}],"links":{"html":"https://tttkmbb.com/geometry/parallelogram","markdown":"https://tttkmbb.com/geometry/parallelogram.md","json":"https://tttkmbb.com/geometry/parallelogram.json","api":"https://tttkmbb.com/api/v1/calculate/parallelogram","schema":"https://tttkmbb.com/api/v1/calculators/parallelogram","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:25:41Z","next_actions":[{"tool":"run_calculator","calculator_id":"parallelogram","reason":"Run Parallelogram Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/geometry/parallelogram.md"}}