Find trapezoid area from its parallel bases and perpendicular height, with the midsegment shown as a check.
Bases 8 and 6 with height 6 give area 42 square units. Average the bases, then multiply by the perpendicular height.
Average base 7 units × height 6 units.
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How to Use the Trapezoid Calculator
Identify the two parallel sides, then measure the perpendicular distance between them. Enter those three lengths using the same unit. The tool returns area in square units and the midsegment length in linear units.
The order of the two bases does not change the area. A slanted nonparallel side is not the height.
Why the Trapezoid Area Formula Works
A trapezoid’s area is the average of the parallel bases multiplied by the height. The average base length is also the midsegment length, the segment connecting the midpoints of the nonparallel sides.
The area does not require the lengths of the slanted sides.
Worked Example: Bases 8 and 6, Height 6
Add the parallel bases: 8 + 6 = 14. Divide by 2 to get the average base: 14 ÷ 2 = 7. Multiply by the perpendicular height: 7 × 6 = 42 square units.
This answer lies between the areas of rectangles with the smaller and larger base at the same height: 6 × 6 = 36 and 8 × 6 = 48 square units.
Can These Inputs Also Determine Perimeter?
No. Base lengths and height determine area, but many trapezoids can share those measurements while having different slanted sides. To find perimeter, you must know all four side lengths. If you have those lengths, use the separate perimeter calculator.
Trapezoid Units and Input Checks
Length inputs must be positive and use the same unit. For bases and height in centimeters, the midsegment is in centimeters and area is in square centimeters. If the two bases happen to be equal, the area formula still evaluates to base × height, as it does for a parallelogram.
Trapezoid Calculator FAQs
What is the formula for trapezoid area?
Area equals half the sum of the two parallel bases times the perpendicular height.
Is a slanted side the height?
No. Height is perpendicular to the parallel bases.
What is the midsegment?
Its length is the average of the two parallel bases.
Editorial review
SolverCalc names Prof. Dr. Khalil Mudassar as its educational reviewer. The formulas and examples are documented in the references below.
Sources
Disclaimer
For educational use. Check your class or textbook convention when the problem defines a different range, sequence index, or notation.