Trapezoid Calculator

Calculate trapezoid area from its two parallel bases and perpendicular height. Find the midline length, or add both legs to calculate the perimeter.

Calculate Your Trapezoid

Enter the lengths of the parallel sides and the shortest distance between them. The height is perpendicular to both bases.

a b h c d
a and b are parallel bases; c and d are legs. Dashed horizontal line = midline. Reference diagram is not drawn to scale.
Optional: calculate perimeter

Enter both nonparallel side lengths. Leave them blank if you only need area and midline.

Inputs can use different units. Changing an input unit converts its measurement. Results update automatically.

Measuring an entire room? Use the square footage calculator to combine areas for your project.

QUICK START

How to Use the Trapezoid Calculator

Start with the parallel bases and perpendicular height. Add the two leg lengths only when you also need the perimeter.

  1. Identify the two parallel bases

    Enter their lengths as base a and base b. Either base can go in either field. Use the parallel sides, rather than the two connecting legs.

  2. Enter the perpendicular height

    Height is the shortest distance between the parallel bases, measured at 90° to them. A sloping leg is not the height. Select the matching unit beside each measurement.

  3. Add both legs if you need perimeter

    Enter c and d in the optional fields. Leave them blank for area and midline only. If the leg lengths conflict with the bases and height, the calculator displays a measurement warning.

  4. Choose result units and review the working

    Select your result units and decimal places. Area uses square units; midline and perimeter use length units. Follow the calculation steps, then select Copy Result to copy your results.

Use consistent measurements: The tool converts mixed units automatically. Its optional-leg check uses a small numerical tolerance, not a general allowance for measurement error. Rounded measurements may trigger a warning even when the real shape is a trapezoid.

WORKED EXAMPLES

Trapezoid Calculations Step by Step

Average the parallel bases and multiply by perpendicular height to find area. For perimeter, add all four sides. Convert mixed measurements to consistent units first.

EXAMPLE 01 · AREA & PERIMETER

Calculate a trapezoid’s area and boundary length

An isosceles trapezoid has parallel bases of 8 cm and 14 cm, a height of 4 cm and two legs of 5 cm each.

GIVEN MEASUREMENTS
Parallel bases
8 cm, 14 cm
Perpendicular height
4 cm
Legs c and d
5 cm each
  1. Find the midline

    m = (a + b) ÷ 2

    m = (8 + 14) ÷ 2 = 11 cm

  2. Multiply by perpendicular height

    A = m × h = 11 × 4

    A = 44 cm²

  3. Add the four sides

    P = 8 + 14 + 5 + 5 = 32 cm

RESULT Area = 44 cm² · Perimeter = 32 cm

Midline = 11 cm. The height measures the distance between the bases; each sloping leg is 5 cm.

EXAMPLE 02 · MIXED UNITS

Find area when the measurements use different units

A trapezoid has bases of 80 cm and 1.4 m. Its perpendicular height is 50 cm. Calculate the area in square meters.

GIVEN MEASUREMENTS
Base a
80 cm
Base b
1.4 m
Perpendicular height
50 cm
  1. Convert all lengths to meters

    a = 80 cm = 0.8 m

    h = 50 cm = 0.5 m

  2. Average the parallel bases

    m = (0.8 + 1.4) ÷ 2 = 1.1 m

  3. Calculate the area

    A = 1.1 × 0.5 = 0.55 m²

RESULT Area = 0.55 m²

Midline = 1.1 m. Perimeter requires the two leg lengths, which are not given here.

Changing the base order does not change the area

The formula adds a and b, so either parallel side can be entered first. With bases of 8 cm and 14 cm, both orders give the same midline of 11 cm. Enter your trapezoid measurements to calculate area and review the working.

UNDERSTAND THE FORMULAS

Trapezoid Area, Midline and Perimeter Formulas

Area depends on the parallel bases and perpendicular height. Perimeter depends on all four side lengths. The midline connects the midpoints of the legs.

a b m h A = m × h
Average the bases to find the midline m = (a + b) ÷ 2. Multiplying this average width by the height gives A = (a + b)h ÷ 2.
a b c d P = a + b + c + d
Perimeter follows the entire boundary Add both bases and both legs. Height is an internal perpendicular distance and is not an extra side to add.
a and b = parallel bases, h = perpendicular height, c and d = legs, m = midline, A = area and P = perimeter. Illustrations do not imply that every trapezoid is symmetric.
Measurement Formula What you need
Area A = (a + b)h ÷ 2 Both bases and height
Midline m = (a + b) ÷ 2 Both bases
Area from midline A = mh Midline and height
Perimeter P = a + b + c + d All four sides
Height from area h = 2A ÷ (a + b) Area and both bases
Missing base b b = 2A ÷ h − a Area, height and base a

Why does the area formula divide by two?

Join a trapezoid to a congruent copy rotated by 180°. Together they form a parallelogram with base a + b and height h. Its area is (a + b)h, so the original trapezoid has half that area.

Equal legs are a special case

For an isosceles trapezoid with unequal bases, each horizontal offset is |b − a| ÷ 2. Each leg therefore has length √[h² + ((b − a)/2)²]. This formula assumes symmetry and should not be used for a general trapezoid.

Manual rearrangements: The height and missing-base formulas are reference calculations; the tool above takes both bases and height as inputs. Use consistent units and check that any calculated base or height is positive.

COMMON QUESTIONS

Frequently Asked Questions

Answers about parallel bases, height, midline, perimeter and optional measurement checks.

Which sides should I enter as the bases?

Enter the two parallel sides as a and b. Either can go first because the formula adds them. The connecting sides are the legs, c and d. Rotating the shape does not change which sides are its parallel bases.

How do I calculate the area of a trapezoid?

Use A = (a + b)h ÷ 2. Add the parallel base lengths, divide by two and multiply by perpendicular height. For another textbook explanation, see OpenStax’s lesson on trapezoid properties and area. Convert all lengths to consistent units before doing the calculation manually.

Can I use a sloping leg as the height?

Only if that leg is perpendicular to both bases, as in a right trapezoid. Otherwise, a sloping leg is longer than the height and cannot replace it in the area formula. Height is the shortest distance between the lines containing the bases.

Why are the leg fields optional?

Area uses only the bases and perpendicular height. Midline uses only the bases. Perimeter needs all four side lengths, so both legs are required for that result. Bases and height alone do not uniquely determine a general trapezoid’s perimeter.

What does the midline represent?

The midline, also called the midsegment, connects the midpoints of the legs. It is parallel to the bases and has length m = (a + b) ÷ 2. Multiplying it by the height gives the area: A = mh.

Why do my optional legs trigger a warning?

A leg cannot be shorter than the perpendicular height. Both leg lengths must also be geometrically consistent with the base difference and height. Check your units and measurements. The test uses a small numerical tolerance, so rounded measurements may trigger a warning. Area still uses the entered bases and height; a warning does not confirm that all five measurements describe one shape.

Can I calculate height from a known area?

Yes, manually rearrange the formula to h = 2A ÷ (a + b). For area 44 cm² and bases 8 cm and 14 cm, h = 88 ÷ 22 = 4 cm. The calculator above takes height as an input; it does not have a separate solve-for-height mode.

Does this work with equal bases or a trapezium?

With equal parallel bases, the area formula reduces to A = ah, the parallelogram formula. Whether that shape is called a trapezoid depends on the definition used. In British usage, a trapezium commonly means a quadrilateral with a pair of parallel sides. Check the shape rather than relying on the name: this tool requires parallel bases and their perpendicular separation.

HAVE YOUR MEASUREMENTS READY?

Find Your Trapezoid’s Area and Midline

Enter the parallel bases and perpendicular height. Add both leg lengths if you also need the perimeter, then follow the calculation steps.

Use Trapezoid Calculator