Geometry
Trapezoid Area Calculator
Area of any trapezoid from parallel sides and height. Compute the area of a trapezoid using A = ½(a+b)h, plus perimeter and diagonal lengths.
Live Vector System
Core Dimensions
Analytic Metrics
Surface Area
78.54
Perimeter
31.416
Mathematical Verification
Our engine utilizes double-precision floating-point arithmetic for geometric derivations. For triangles, we implement Heron's Theorem with strict validation to ensure the triangle inequality principle is maintained.
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Solution Methodology
01
Enter Bases & Height
Input parallel side a, parallel side b, and perpendicular height h.
02
Compute Area
Apply A = ½(a + b)h and display the midsegment (a+b)/2.
03
Compute Perimeter
Derive leg lengths from height and base offset, then sum all four sides.
Common Questions
What is the formula for the area of a trapezoid?
Area = ½ × (a + b) × h, where a and b are the lengths of the two parallel sides and h is the perpendicular height between them. This formula averages the two bases and multiplies by the height, similar to a rectangle formula but accounting for the unequal sides.
How do you find the height of a trapezoid if not given?
If you know the leg length l and the difference in bases, you can find h using the Pythagorean theorem: h = √(l² − d²) where d is the horizontal offset of the leg. Alternatively, use the law of cosines if an interior angle is known.