Geometry

Trapezoid Area Calculator

What this does

Find trapezoid area from its two parallel bases and height using the averaged-base formula.

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Calculator inputs

How to use it

Using the trapezoid area calculator

  1. 01

    Identify the parallel sides

    These are your two bases regardless of orientation.

  2. 02

    Measure the perpendicular height

    Straight across between the bases, not along a slant.

  3. 03

    Read the area

    In squared units; the average-base row shows the intermediate quantity.

Good to know

Where trapezoids hide in plain sight

Road cross-sections, retaining-wall faces, roof gables, irrigation channels and hand-drawn area sketches under curves are all trapezoids. The shape is also the workhorse of the trapezoidal rule in numerical integration; approximating curved regions by stacking many thin trapezoids.

Height versus slant length

Measuring along the slanted leg inflates area because the leg runs diagonal to the bases. If you only know legs and angles, compute the true height first (leg × sin θ); otherwise estimates run high by the cosine factor.

How it's calculated

The math behind this calculator

A = ½(a + b) × h

A trapezoid’s area equals its average base width times its height: half the sum of the parallel sides multiplied by their perpendicular separation. Intuition: it is a rectangle whose top edge was widened or narrowed, so averaging the two edges recovers the mean footprint.

The height must be measured perpendicular to both bases, not along a slanted leg; a common field-measurement mistake that overestimates area.

Assumptions & limitations

  • The two bases entered are the parallel sides.
  • Height is the perpendicular distance between them.
  • All lengths positive and consistently unit-ed.

Worked example

Parallel sides of 10 and 6 separated by a height of 5 give an area of 40 square units; the average base of 8, times 5.

FAQ

Frequently asked questions

What if both bases are equal?
Then it is a parallelogram and the formula gracefully reduces to base × height.
Does the shape need to be symmetric?
No; as long as two sides are parallel and you have the perpendicular height, the slanted legs’ angles are irrelevant.
Can I use it for sloped land area?
For a plot bounded by two parallel lines, yes; that cross-section is exactly a trapezoid.
Which sides are “bases”?
Always the two parallel ones. Swapping a and b changes nothing since they are summed.

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