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Calculator Answers

Trapezoid Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A trapezoid calculator is a geometric tool that computes the area, perimeter, side lengths, and angles of a trapezoid. By entering the lengths of the two parallel bases and the height, the calculator determines the area using the formula where area equals the average of the bases multiplied by the height. It can also solve for missing angles or side lengths if coordinate points or side inputs are provided. Students and draftspersons use this tool to solve geometry homework and estimate land plots.

Enter the two parallel bases and the height to get the area. Add the two non-parallel sides for the perimeter.

See also: Area Calculator – Find the Area of a Shape, Triangle Area Calculator, and Perimeter Calculator.

Quick Answer

Calculate the area and dimensions of a trapezoid. Enter the bases and height to find the area and perimeter with formulas.

One of the two parallel sides. · e.g. 8

The other parallel side. · e.g. 12

Perpendicular distance between the bases. · e.g. 5

For perimeter. · e.g. 6

For perimeter. · e.g. 7

Area uses the two bases and the height. Add both non-parallel sides to also see the perimeter.

Trapezoid

Area

50

((8 + 12) ÷ 2) × 5

Base 18
Base 212
Height5
Average base10
Area50

Area = ((base 1 + base 2) ÷ 2) × height. Perimeter sums all four sides when both non-parallel sides are entered.

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Examples

Bases 8 & 12, height 5

area 50

Bases 10 & 14, height 6, sides 7 & 7

area 72 · perimeter 38

Bases 3 & 9, height 4

area 24

How it works

Formula · Area = ((b1 + b2) / 2) x h, the average of the two parallel bases times the perpendicular height. Perimeter = b1 + b2 + leg1 + leg2, and needs both legs.

A trapezoid has one pair of parallel sides (bases) and a height perpendicular to them. Area uses the average of the two bases, multiplied by the height. Perimeter sums all four sides directly.

Area · A = ((base 1 + base 2) ÷ 2) × height

Perimeter · P = base 1 + base 2 + side 1 + side 2

Height is perpendicular to the bases, not the slant side.

Why the formula averages the two bases

A trapezoid has two parallel sides of different lengths, so there is no single width to multiply by the height. The formula takes the average of the two instead: add the bases, halve them, and multiply by the height.

The reason it works is worth seeing once. Take a copy of the trapezoid, turn it upside down, and set it beside the original. The short base of one now sits against the long base of the other, so the pair together form a parallelogram whose width is the two bases added and whose height is unchanged. That parallelogram has area (b₁ + b₂) × h, and your trapezoid is exactly half of it. Averaging the bases is the same step as halving that doubled shape.

Working an area out by hand

Bases of 8 and 12, with a height of 5.

  1. Add the two bases. 8 + 12 = 20.
  2. Halve that to get the average width. 20 ÷ 2 = 10.
  3. Multiply by the height. 10 × 5 = 50, so the area is 50 square units.

The perimeter is a separate question and needs two more numbers. Adding the two non-parallel sides, the legs, to the two bases gives it, which is why this calculator shows a perimeter only once both legs have been entered. The bases and the height alone cannot determine it: many different trapezoids share them.

Edge cases, and what the answer means

  • Equal bases. If both bases are the same length the shape is a parallelogram, and if its corners are square it is a rectangle. The formula still works: averaging two equal numbers returns that number, so it collapses to width times height, which is the rectangle formula.
  • The height is perpendicular, not slanted. The height is the straight-up distance between the two parallel sides, measured at a right angle to them. It is not the length of a sloping leg. Using a leg by mistake always overstates the area, and on a steeply slanted trapezoid it overstates it badly.
  • Perimeter needs both legs. Enter one leg and no perimeter appears, because the fourth side is still unknown. This is a deliberate refusal rather than a gap.
  • Zero or negative inputs. A base or height of zero leaves no shape to measure, so it is rejected rather than returning an area of zero.

Your measurements stay in the page

Every measurement you enter is processed by this page in your browser. The bases, the height, the legs and the result are not sent to a server, not stored after you close the tab, and not visible to anyone else. There is no account and nothing to sign up for.

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Area Calculator – Find the Area of a ShapeFind the area of a shape from one tool. Supports circle, triangle, rectangle, and other common 2D geometric shapes.Triangle Area CalculatorCalculate the area of any triangle from base and height, three sides (Heron's formula), or two sides and the included angle (SAS).Perimeter CalculatorCalculate the perimeter (or circumference) of common 2D shapes: rectangle, triangle, circle, trapezoid, parallelogram, and regular polygon.Parallelogram CalculatorCalculate the area, perimeter, and interior angle of a parallelogram from base, height, and slant side.

Frequently asked questions

Mostly which country you are in. In American usage a trapezoid is a quadrilateral with one pair of parallel sides, and that is what this calculator computes. In British usage that same shape is called a trapezium, and trapezoid there means a quadrilateral with no parallel sides at all. If you arrived here searching for a trapezium area, this is the page you want.

Square units of whatever you entered. Bases and height in metres give square metres; in inches, square inches. The calculator does not convert between units, so measure the two bases and the height in the same one before entering them.

Use the area calculator when you need several different shapes, or a shape this page does not cover. Use this page when the shape is a trapezoid and you also want the perimeter, since that needs the two legs and is not part of a general area tool's job.

Because the shape has two different widths and needs one number to multiply the height by. Take a second copy of the trapezoid, flip it, and set it against the first: together they make a parallelogram of width b₁ + b₂ and the same height. That doubled shape has area (b₁ + b₂) × h, and one trapezoid is half of it. Averaging the bases and multiplying by the height is the same calculation.

Because the bases and the height do not determine the legs. Many different trapezoids share the same two bases and the same height while leaning at different angles, and each has a different perimeter. The calculator shows a perimeter once both non-parallel sides are supplied, and stays silent until then rather than guessing.

No, and confusing the two is the most common error with this shape. The height is the perpendicular distance between the two parallel sides, measured straight across at a right angle. A slanted leg is always longer than that perpendicular distance, so using it in place of the height overstates the area, and the more the shape leans the worse the overstatement gets.

The shape becomes a parallelogram, or a rectangle if the corners are square, and the formula still gives the right answer. Averaging two equal numbers returns that same number, so the calculation collapses to width times height. Nothing special is needed for the case.

Yes. The area formula only cares about the two parallel sides and the perpendicular distance between them, so it holds whether the legs are equal, unequal, or one of them is vertical. A right trapezoid, where one leg meets the bases at a right angle, is just the case where that leg equals the height.

A trapezoid (called a trapezium in British English) is a four-sided polygon with exactly one pair of parallel sides. The parallel sides are called bases; the non-parallel sides are called legs. The height is the perpendicular distance between the two bases.

Take the average of the two parallel bases and multiply by the height: A = ((base 1 + base 2) ÷ 2) × height. For bases 8 and 12 with height 5, the area is ((8 + 12) ÷ 2) × 5 = 10 × 5 = 50 square units.

Add all four sides: P = base 1 + base 2 + side 1 + side 2. The two non-parallel sides (legs) are not equal to the height; the height is perpendicular to the bases while the legs slant. Enter both side lengths to get the perimeter.

An isosceles trapezoid has two equal non-parallel sides. The formulas are the same: enter the same value for both sides and the calculator returns the symmetric result. The same area formula works because it depends only on the bases and height.

A trapezoid is like a rectangle with one base that varies linearly from base 1 to base 2. Averaging the two bases gives the effective width of an equivalent rectangle with the same area, and multiplying by the height completes the area.

Technically a parallelogram has two pairs of parallel sides, so if you enter base 1 = base 2, the area reduces to base × height, which is the parallelogram formula. For a dedicated parallelogram calculator with its own input style, use the parallelogram calculator.