📏 Enter known values

📐 Accepted units: mm, cm, dm, m, dam, hm, km, in, ft, yd, mi

Formula Reference

render

Worked example

Data
Base 1
\(b = {\color{#6c5ce7}{8\,\text{cm}}}\)
Base 2
\(c = {\color{#6c5ce7}{4\,\text{cm}}}\)
Side 1
\(d = {\color{#6c5ce7}{3\,\text{cm}}}\)
Side 2
\(e = {\color{#6c5ce7}{3\,\text{cm}}}\)
Perimeter
\(a = \,?\)
Formula
\[a = {b}+{c}+{d}+{e}\]
Steps
1Substitute the values
\[a = {\color{#6c5ce7}{8\,\text{cm}}}+{\color{#6c5ce7}{4\,\text{cm}}}+{\color{#6c5ce7}{3\,\text{cm}}}+{\color{#6c5ce7}{3\,\text{cm}}}\]
Each letter is replaced by its value.
2Add
\[a = {\color{#6c5ce7}{8\,\text{cm}}}+{\color{#6c5ce7}{4\,\text{cm}}}+{\color{#6c5ce7}{3\,\text{cm}}}+{\color{#6c5ce7}{3\,\text{cm}}} = 18\,\text{cm}\]
\(8+4 = 12\)\(12+3 = 15\)\(15+3 = 18\)
Perimeter: 18 cm
Check

If we use the result to calculate Base 1, we should get the value you entered:

\[b = {a}-{c}-{d}-{e}\]
\[b = 18\,\text{cm}-4\,\text{cm}-3\,\text{cm}-3\,\text{cm} = 8\,\text{cm}\]
It gives 8 cm, the same as the value entered.
Calculate the Perimeter
Please fill in the fields:
Base_1 Base_2 Side_1 Side_2
And leave empty
Perimeter
Calculate the Base_1
Please fill in the fields:
Perimeter Base_2 Side_1 Side_2
And leave empty
Base_1
Calculate the Base_2
Please fill in the fields:
Perimeter Base_1 Side_1 Side_2
And leave empty
Base_2
Calculate the Side_1
Please fill in the fields:
Perimeter Base_1 Base_2 Side_2
And leave empty
Side_1
Calculate the Side_2
Please fill in the fields:
Perimeter Base_1 Base_2 Side_1
And leave empty
Side_2

How to calculate the perimeter of a trapezoid

The perimeter of any trapezoid is the sum of its four sides: the two parallel bases and the two non-parallel sides, also called legs:

\[ P = \text{Base}_1 + \text{Base}_2 + \text{Side}_1 + \text{Side}_2 \]

If you know the perimeter and three sides, the missing side is the perimeter minus the other three:

\[ \text{Side}_2 = P - \text{Base}_1 - \text{Base}_2 - \text{Side}_1 \]

How to use the calculator

  1. Enter four of the five values.
  2. Leave empty the one you want to find.
  3. Press Calculate. All the sides must be in the same unit.

Worked examples

1. Bases of 10 cm and 6 cm and sides of 5 cm and 4 cm

\[ P = 10 + 6 + 5 + 4 = 25\ \text{cm} \]

2. Missing side with a perimeter of 40 m

Bases of 15 m and 9 m and one side of 7 m: \( 40 - 15 - 9 - 7 = 9 \) m.

3. Isosceles trapezoid

In an isosceles trapezoid both legs are equal, so \( P = B_1 + B_2 + 2s \). With bases of 12 and 8 and legs of 5, \( P = 12 + 8 + 2 \times 5 = 30 \).

When you know the height instead of the legs

In an isosceles trapezoid, each leg is the hypotenuse of a right triangle formed by the height and half the difference of the bases:

\[ s = \sqrt{h^2 + \left(\frac{B_1 - B_2}{2}\right)^2} \]

Example: bases of 14 and 8 and a height of 4. Each leg is \( \sqrt{4^2 + 3^2} = 5 \), so the perimeter is \( 14 + 8 + 5 + 5 = 32 \).

In a right trapezoid, one leg is the height itself and the other is \( \sqrt{h^2 + (B_1 - B_2)^2} \). With bases of 10 and 4 and a height of 8, the slanted leg is \( \sqrt{64 + 36} = 10 \) and the perimeter is \( 10 + 4 + 8 + 10 = 32 \).

Types of trapezoid

  • Isosceles: equal legs and equal angles at each base.
  • Right: one leg is perpendicular to the bases.
  • Scalene: all four sides are different.

When Do You Need to Calculate the Perimeter of a Trapezoid?

🏡 Fencing Irregular Plots

Many plots have two parallel boundaries and two slanted ones. The perimeter is the total length of fence or wall needed to enclose them.

Accurate fencing quotes for irregular lots
🏠 Roof Edges and Flashing

The faces of hip roofs are trapezoids. Their perimeter gives the length of flashing, gutters and edge trim along each face.

Order gutters and trim for each roof face
🪟 Windows and Frames

Trapezoidal windows under gables and in modern designs need frames and seals along all four sides.

Cut frames and weather seals to length
🌾 Garden Beds and Ponds

Beds and ponds built in a trapezoidal shape need edging and borders around their perimeter.

Plan edging and borders
👜 Bags and Lampshades

Bag panels and lampshade sides are often trapezoids. The perimeter tells how much piping, zipper or trim goes around each piece.

Buy the right length of trim
📚 Geometry Problems

Exercises often give the height of an isosceles or right trapezoid instead of its legs, so you need the Pythagorean theorem first.

Combines perimeter with right triangles

Common Mistakes

⚠️ Leaving Out a Side
Common Error: Adding only the two bases and one leg. A trapezoid always has four sides.
✅ Solution: Add the two bases and both legs
⚠️ Using the Height as a Leg
Common Error: The height is perpendicular to the bases; the legs are slanted and longer, except in a right trapezoid.
✅ Solution: Measure the legs along the edge, or calculate them from the height
⚠️ Assuming Equal Legs
Common Error: Doubling one leg when the trapezoid is not isosceles.
✅ Solution: Measure both legs unless you know it is isosceles
⚠️ Using the Area Formula
Common Error: Applying (B₁ + B₂) × h ÷ 2, which is the area, not the perimeter.
✅ Solution: The perimeter adds the four sides
⚠️ Using the Full Difference of the Bases
Common Error: In an isosceles trapezoid, using B₁ − B₂ instead of half of it to find the legs from the height.
✅ Solution: Each leg covers (B₁ − B₂) ÷ 2 horizontally
⚠️ Mixed Units
Common Error: Bases measured in meters and legs in centimeters on a plan.
✅ Solution: Convert all sides to one unit

Applications by Industry

Construction
  • Roofing: Edge trim and flashing for trapezoidal roof faces
  • Walls: Perimeter of gable walls for corner beads and seals
  • Formwork: Boards around trapezoidal footings
Surveying
  • Lots: Boundary length of trapezoidal plots
  • Fencing: Posts and wire along irregular boundaries
  • Roads: Edges of trapezoidal medians and islands
Hydraulics
  • Channels: Wetted perimeter of trapezoidal canals, used in flow formulas
  • Ponds: Liner edges for trapezoidal ponds
  • Drainage: Length of ditch lining
Manufacturing
  • Sheet metal: Edge length to weld or fold on trapezoidal blanks
  • Hoppers: Seams of tapered hoppers and ducts
  • Gaskets: Seals for trapezoidal hatches
Design & Crafts
  • Bags: Piping around trapezoidal panels
  • Lampshades: Trim for tapered panels
  • Furniture: Edge banding for trapezoidal tabletops
Education
  • Geometry: Perimeter of quadrilaterals
  • Pythagorean theorem: Finding the legs from the height
  • Algebra: Solving for a missing side

External Resources

Other calculators

Perimeter of a Square
Perimeter of a Square
Perimeter of a Rhombus
Perimeter of a Rhombus
Perimeter of a Triangle
Perimeter of a Triangle
Perimeter of a Rectangle
Perimeter of a Rectangle
Perimeter of a Rhomboid
Perimeter of a Rhomboid
Perimeter of a Circle
Perimeter of a Circle
Internal Angles of a Quadrilateral
Internal Angles of a Quadrilateral
Area of a Rectangle
Area of a Rectangle

Geometry Calculators

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