{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"trapezoid"},"result":{"entity_type":"calculator","id":"trapezoid","calculator_id":"trapezoid","canonical_url":"https://tttkmbb.com/geometry/trapezoid","name":"Trapezoid Calculator","title":"Trapezoid Calculator – Area from Parallel Sides and Height, Perimeter with Legs","category":"geometry","category_name":"Geometry","tool_name":"calculate_trapezoid_properties","featured_mcp_tool":false,"description":"Computes the area and midsegment of a trapezoid (trapezium) from its two parallel sides and height, and the perimeter when both non-parallel legs are given.","use_when":"You need the area of a quadrilateral with exactly one pair of parallel sides, or its perimeter when all four sides are known.","do_not_use_when":"Both pairs of sides are parallel (use parallelogram or rectangle) or you only know the four sides without the height (the height cannot be derived without an angle in general).","inputs":[{"name":"base_a","label":"Base a","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"First parallel side.","example":8},{"name":"base_b","label":"Base b","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Second parallel side.","example":5},{"name":"height","label":"Height","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Perpendicular distance between the two parallel sides.","example":4},{"name":"leg_c","label":"Leg c","type":"number","unit":"units","required":false,"exclusive_min":0,"description":"First non-parallel side (optional, needed for the perimeter).","example":4.5},{"name":"leg_d","label":"Leg d","type":"number","unit":"units","required":false,"exclusive_min":0,"description":"Second non-parallel side (optional, needed for the perimeter).","example":5}],"outputs":[{"name":"area","label":"Area","type":"number","unit":"units²","decimals":4,"description":"(base_a + base_b) / 2 × height."},{"name":"midsegment","label":"Midsegment","type":"number","unit":"units","decimals":4,"description":"Segment joining the midpoints of the legs = (base_a + base_b) / 2."},{"name":"perimeter","label":"Perimeter","type":"number","unit":"units","decimals":4,"description":"base_a + base_b + leg_c + leg_d (only when both legs are given)."}],"input_schema":{"type":"object","properties":{"base_a":{"description":"First parallel side. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[8],"x-unit":"units"},"base_b":{"description":"Second parallel side. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[5],"x-unit":"units"},"height":{"description":"Perpendicular distance between the two parallel sides. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[4],"x-unit":"units"},"leg_c":{"description":"First non-parallel side (optional, needed for the perimeter). Unit: units.","type":"number","exclusiveMinimum":0,"examples":[4.5],"x-unit":"units"},"leg_d":{"description":"Second non-parallel side (optional, needed for the perimeter). Unit: units.","type":"number","exclusiveMinimum":0,"examples":[5],"x-unit":"units"}},"additionalProperties":false,"required":["base_a","base_b","height"]},"output_schema":{"type":"object","properties":{"area":{"description":"(base_a + base_b) / 2 × height. Unit: units².","type":"number","x-unit":"units²"},"midsegment":{"description":"Segment joining the midpoints of the legs = (base_a + base_b) / 2. Unit: units.","type":"number","x-unit":"units"},"perimeter":{"description":"base_a + base_b + leg_c + leg_d (only when both legs are given). Unit: units.","type":"number","x-unit":"units"}}},"formula":"area = (base_a + base_b) / 2 × height; midsegment = (base_a + base_b) / 2; perimeter = base_a + base_b + leg_c + leg_d","method":"Each leg must be at least as long as the height (a leg equal to the height is perpendicular to the bases, as in a right trapezoid).","sources":[{"name":"Wikipedia – Trapezoid","url":"https://en.wikipedia.org/wiki/Trapezoid","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wolfram MathWorld – Trapezoid","url":"https://mathworld.wolfram.com/Trapezoid.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":"Bases 8 and 5, height 4, legs 4.5 and 5","inputs":{"base_a":8,"base_b":5,"height":4,"leg_c":4.5,"leg_d":5},"expected":{"area":26,"midsegment":6.5,"perimeter":22.5},"url":"https://tttkmbb.com/api/v1/calculate/trapezoid?base_a=8&base_b=5&height=4&leg_c=4.5&leg_d=5"},{"name":"Bases 10 and 6, height 3","inputs":{"base_a":10,"base_b":6,"height":3},"expected":{"area":24,"midsegment":8},"url":"https://tttkmbb.com/api/v1/calculate/trapezoid?base_a=10&base_b=6&height=3"}],"faq":[{"q":"Trapezoid or trapezium?","a":"In US usage a trapezoid has one pair of parallel sides; in British usage that shape is called a trapezium. This calculator uses the one-pair-of-parallel-sides definition."},{"q":"Can I get the area from four sides only?","a":"Not in general: the shape is not rigid unless which sides are parallel and the height (or an angle) are known. Enter the height directly."}],"tags":["trapezoid","trapezium","area of a trapezoid","parallel sides","midsegment"],"related":[{"calculator_id":"parallelogram","reason":"Both pairs of sides parallel."},{"calculator_id":"triangle-area","reason":"A trapezoid with one base of length 0 is a triangle."}],"links":{"html":"https://tttkmbb.com/geometry/trapezoid","markdown":"https://tttkmbb.com/geometry/trapezoid.md","json":"https://tttkmbb.com/geometry/trapezoid.json","api":"https://tttkmbb.com/api/v1/calculate/trapezoid","schema":"https://tttkmbb.com/api/v1/calculators/trapezoid","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:24:36Z"}