Calculate the area, perimeter, diagonals, height, median, and angles of an isosceles trapezoid from its parallel sides and leg or height.
An isosceles trapezoid is a quadrilateral with one pair of parallel sides (called bases) and two non-parallel sides (legs) of equal length. This symmetry gives it special properties: equal base angles, equal diagonals, and a perpendicular line of symmetry through the midpoints of the two bases.
The area of an isosceles trapezoid is calculated using the formula A = ½(a + b) × h, where a and b are the lengths of the parallel sides and h is the perpendicular height between them. When the leg length is known instead of the height, the height can be derived using the Pythagorean theorem: h = √(l² − ((b − a)/2)²), where l is the leg length.
This calculator supports two input modes: entering the parallel sides with the leg length, or entering the parallel sides with the height directly. In both cases it computes the full set of properties including area, perimeter, diagonal length, the median (midsegment), and both base and top angles. The diagonal of an isosceles trapezoid is given by d = √(l² + a·b). The median — the segment connecting the midpoints of the legs — equals the average of the two bases: m = (a + b)/2.
Isosceles trapezoids appear in architecture, road cross-sections, bridge trusses, and decorative design. Understanding their measurements is essential in civil engineering, carpentry, and land surveying.
Isosceles Trapezoid Area problems often require several dependent steps, and a small arithmetic slip can propagate through every derived value. This calculator is tailored to that workflow: you enter top side a (value), bottom side b (value), leg length (value), and it returns area, perimeter, height, diagonal in one consistent pass. It is useful for homework checks, worksheet generation, tutoring walkthroughs, and fast field/design estimates where you need reliable geometry results without rebuilding the full derivation each time.
Area = ½ × (a + b) × h, where a and b are the parallel sides and h is the height. Height from leg: h = √(l² − ((b − a)/2)²). Diagonal: d = √(l² + a·b). Median: m = (a + b)/2.
Result: Area ≈ 36.66 cm²
Height = √(5² − ((10−6)/2)²) = √(25 − 4) = √21 ≈ 4.583 cm. Area = ½ × (6 + 10) × 4.583 ≈ 36.66 cm².
This isosceles trapezoid area tool links the entered values (top side a (value), bottom side b (value), leg length (value), height h (value)) to the target geometry relationships used in class and practice problems. Instead of solving each intermediate step manually, you can validate setup and arithmetic quickly while still tracing which measurements drive the final result.
Formula focus: the calculator formula
Isosceles Trapezoid Area shows up in school geometry, technical drafting, construction layout checks, and early engineering design estimates. When values are changed repeatedly, the calculator helps you compare scenarios quickly and see how sensitive the shape is to each dimension.
Start with the primary outputs (area, perimeter, height, diagonal) and then use the remaining cards/tables to confirm consistency with your diagram. Keep units consistent across inputs, and round only at the end if your assignment or project specifies a fixed precision.
An isosceles trapezoid has two non-parallel sides (legs) of equal length, giving it a line of symmetry perpendicular to the bases. Use this as a practical reminder before finalizing the result.
Use h = √(l² − ((b − a)/2)²), where l is the leg length, b is the longer base, and a is the shorter base. Keep this note short and outcome-focused for reuse.
Yes. Equal diagonals are a unique property of isosceles trapezoids among all trapezoids.
The median (or midsegment) connects the midpoints of the two legs and its length equals the average of the two parallel sides. Apply this check where your workflow is most sensitive.
By convention the longer side is called the bottom base. If you swap them, the formulas still work, but the calculator expects a < b.
By dropping a perpendicular from one top vertex to the base, creating a right triangle, and applying the distance formula: d = √(l² + a·b). Use this checkpoint when values look unexpected.