Trapezoid Perimeter Calculator

Calculate the perimeter of a trapezoid from all four sides, from the bases and one leg (isosceles), or from the bases and height (right). Solve for a missing side, plus the median, height, and area.

https://hexacalculator.com/calculators/mathematics/geometry/trapezoid-perimeter-calculator

Mathematics

Geometry

Trapezoid Perimeter Calculator

Calculate the perimeter of a trapezoid from all four sides, from the bases and one leg (isosceles), or from the bases and height (right). Solve for a missing side, plus the median, height, and area.

Trapezoid Perimeter Calculator

Choose what you know about the trapezoid; the calculator shows the right fields and solves for whatever you leave blank.

Enter the two bases and the two legs to get the perimeter. You can also enter the perimeter with three sides to solve for the missing fourth side.

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The perimeter of a trapezoid is the distance around the outside of the shape, calculated by adding together all four sides. When you enter information into this calculator about a trapezoid, it will also give you the length of the midline, height and area.

A trapezoid is a geometric figure with four sides, two of which are parallel to each other. These two parallel sides are called bases, and the shorter side is usually denoted as a while the longer side is denoted as b. The two non-parallel sides that connect the bases are called legs and they are denoted as c and d respectively. There are three ways you can input: You can enter all four sides, for an isosceles trapezoid you can enter both bases and one leg, and for a right trapezoid you can enter both bases and the height.

The formula for perimeter of a trapezoid is:

Sum of both bases and both legs, this is the full formula.

P=a+b+c+dP = a + b + c + d

Here a and b are the parallel bases and c and d are the legs. If the bases are 5 and 10 and the legs are 6 and 7 then the perimeter is 5 + 10 + 6 + 7 = 28. This calculator can also work in reverse: if you enter the perimeter and three of the sides, it will calculate the fourth side by subtraction.

Isosceles trapezoid.

An isosceles trapezoid has two sides of equal length (the legs), so you only need the lengths of both bases and one leg. Double the length of one leg and add that to the lengths of both bases.

P=a+b+2cP = a + b + 2c

If the base sides are 5 and 11 and the equal legs are 5 then the perimeter is 26. If the perimeter and either base side or leg are given, this tool will calculate the missing length.

Calculating a right-angled trapezoid from the height:

A right trapezoid has a base and a leg that is perpendicular to it; this leg corresponds directly to the height h. The other leg runs at an angle, so using Pythagoras' theorem we can calculate its length from the difference between the height and the two bases.

d=h2+(b−a)2P=a+b+h+h2+(b−a)2d = \sqrt{h^2 + (b - a)^2} \qquad P = a + b + h + \sqrt{h^2 + (b - a)^2}

If the base sides are 4 and 10 and the height is 8 then the sloping side is the square root of (64+36) which is 10 so the perimeter is 4+10+8+10 = 32.

Elements of a trapezoid.

In addition to the perimeter, a trapezoid can also be uniquely determined by the length of its sides. In this case, the calculation tool provides additional information about the trapezoid. The median line, also called the connecting segment of the midpoints, is a segment that connects the midpoints of both legs. It runs parallel to the base and has a length equal to the average of the two bases.

m=a+b2m = \frac{a + b}{2}

The altitude is the vertical distance between the two bases. If all four sides are known, then the altitude can be determined by projecting both legs onto the longer base. The difference of the bases is denoted D = b − a, and the length of the horizontal projection of side c is given by:

p=D2+c2−d22Dh=c2−p2p = \frac{D^2 + c^2 - d^2}{2D} \qquad h = \sqrt{c^2 - p^2}

Once the height is known, the area of the trapezoid can be calculated by multiplying the height with the midline, i.e. the average of the bases.

A=a+b2 h=m hA = \frac{a + b}{2}\,h = m\,h

To use the calculator:

If you select a condition above the calculator will only show fields that are required for it. Enter values and leave the field for perimeter blank to calculate perimeter. Alternatively enter a value for perimeter and leave one of the side fields blank to calculate backwards. Each field has an associated unit so the calculator will convert all entered values into a common reference before calculating, even if you enter centimeters for one base and inches for another.

As the trapezoid is uniquely determined by its side lengths, other information than just the perimeter will be shown in the result area. The midline, height, area and both angles at the base sides are shown, as well as whether it's a right-angled, isosceles or scalene trapezoid. In addition to that, you can estimate the cost of fences or decorations by using the perimeter and the price per meter.

Trapezoid types:

If all four sides have different lengths, the trapezoid is a scalene trapezoid. If both legs are of equal length, it is called an isosceles trapezoid. If one leg is perpendicular to the bases, then it's a right trapezoid. Isosceles trapezoids have symmetry, which means that the base angles and diagonals are all congruent. In a right trapezoid, there are two right angles on either side of the leg that is perpendicular to the bases.

If the two parallel sides are exactly equal in length then it is not a trapezoid but a parallelogram. This is because for a shape to be a trapezoid the lengths of the two parallel sides must differ. The calculator will calculate the perimeter, mark this situation and leave height and area blank.

If only the angles are known:

It is possible to have the base side, both legs and one of the base angles known while the other base side is unknown. The height can be calculated from the angle, and with Pythagoras' theorem the length of the line each leg extends in direction of the base can be determined.

h=csin⁡αpc=c2−h2pd=d2−h2h = c \sin\alpha \qquad p_c = \sqrt{c^2 - h^2} \qquad p_d = \sqrt{d^2 - h^2}

If you subtract these two projection lengths from the known base length, you get the other base length, so b = a - p_c - p_d. The perimeter is then found by adding all four sides together. If only angles and one base are given, this information alone does not suffice. The other base and other angles can vary, so at least one length for each leg must be known.

Example calculation:

The table below shows the perimeter of a trapezoid calculated by various methods.

Case

You enter

Perimeter

General

bases 5, 10; legs 6, 7

28

Isosceles

bases 5, 11; equal leg 5

26

Right

bases 4, 10; height 8

32

Solve a side

perimeter 28; sides 5, 10, 6

missing side 7

Use of trapezoidal perimeter:

The perimeter is used when something needs to be placed around the edges of a trapezoid or the edges need to be trimmed. Framing trapezoidal windows or countertops, bordering trapezoidal flowerbeds or patios, and adding borders to trapezoidal signs or banners all require calculating the perimeter and multiplying it by a price per meter. This is what the fence calculator function of this tool is for.

Students use trapezoids in geometry classes and can check their homework using this tool. Construction workers and manufacturers use this tool when they need to create a part with one pair of parallel sides and two sloping sides. Since the length of the sides determines the shape, setting the lengths also sets the perimeter, midline, height, and area.

Tips for accurate results:

Please measure all sides as far as possible with the same unit. Mixing units is the most common cause of incorrect results. Leave the conversion to the calculation tools. Enter the shorter of the parallel sides as "a" and the longer one as "b", and enter both slanted sides as "legs". If you switch base and leg, the shape changes.

If the four sides entered do not form a closed trapezoid, then the calculator will add them to calculate the perimeter but will show a warning and leave the height and area blank. This happens when one of the legs is too short or too long for the endpoints of the two bases to connect.

Frequently asked questions

What is the formula for perimeter of a trapezoid?

Add the four sides together to get the perimeter. P = a + b + c + d, where a and b are the parallel bases and c and d are the legs. If the bases are 5 and 10, and the legs are 6 and 7, then the perimeter is 28. In an isosceles trapezoid, where the two legs have the same length, the formula can be simplified to P = a + b + 2c.

How to calculate the perimeter of an isosceles trapezoid?

Since the lengths of both legs are equal we only need two bases and one leg. We double the length of the leg and add it to the two bases, so P = a + b + 2c. If the bases are 5 and 11 and the congruent legs are 5 then the perimeter is 26. Please select the conditions for an isosceles trapezoid and enter the two bases and one leg.

How do you calculate the perimeter of a right trapezoid?

In a right trapezoid one side is perpendicular to the bases, which represents the height h. The other leg is the square root of h squared plus b minus a squared, and the perimeter is the sum of a plus b plus h plus this leg. Select the conditions for a right trapezoid and enter both bases and the height, then the tool will calculate the other leg.

If you know the perimeter, can you calculate a missing side?

Yes. In general you can enter the perimeter and any three sides and leave the fourth side blank and then the tool will calculate it by subtraction. This also works for isosceles trapezoids. If you enter the perimeter and two bases, the leg can be calculated. If you enter the perimeter, a leg, and one base, the other base can be calculated.

What is a median of a trapezoid?

The median (also called the midsegment) connects the midpoints of two sides and is parallel to the bases. Its length is the average of the two bases: m = (a + b)/2. So, if the bases are 4 and 10, then the median is 7. The area of a trapezoid is calculated by multiplying the median by the height.

Can this calculation tool also determine area?

Yes. If the side lengths uniquely define a trapezoid, then this calculator will use the height to calculate the area. The height is found by multiplying (a + b) / 2 by h. It also displays the midline, the height itself, and both base angles. For a right trapezoid, the height is the entered vertical side.

Can the perimeter only be calculated by using the angles?

No, the perimeter cannot be calculated using only the angles. Since the other base and possibly other angles can vary, at least one length of each side must be known. If a base, both sides, and an included angle are given, then the height is found by multiplying the sine of the angle by side c, and the other base can be found from the projection of the two sides using the Pythagorean theorem.

Related calculators

Trapezoid Area CalculatorFind the area of a trapezoid from its two bases and height, or enter the area to solve for a missing base or the height. Also gives the median, perimeter, legs, base angles, and diagonal.
Base of a Triangle CalculatorFind the base of a triangle from its area and height, or from two equal sides, a right-angle hypotenuse, the perimeter, or a side and two angles. Solve for the area or height too.
Triangle Perimeter CalculatorFind the perimeter of a triangle three ways: from one side of an equilateral triangle, from the equal sides and base of an isosceles triangle, or from the three sides of a scalene triangle. Also gives the area, semi-perimeter, angles, heights, medians, and circles, and estimates a fencing cost.
Area CalculatorFind the area of a square, rectangle, triangle, circle, sector, ellipse, trapezoid, parallelogram, or rhombus. Pick a shape, enter its measurements, and get the area and perimeter in any unit.
Square Perimeter CalculatorFind the perimeter of a square from the side, area, diagonal, or perimeter, with every other measurement alongside, in any unit.
Rhombus Perimeter CalculatorFind the perimeter of a rhombus from one side, the perimeter, or both diagonals, with the area, angles, and height alongside, in any unit.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

  1. Wikipedia: Trapezoid

    Definition of a trapezoid, its bases, legs, median, height, and the main types.

  2. Wikipedia: Perimeter

    The perimeter of a polygon as the sum of its side lengths.

  3. Math is Fun: Trapezoid

    Plain-language explanation of the trapezoid, its median, area, and perimeter.