Perimeter of Trapezoid Calculator
Enter all four sides, or the bases and height of an isosceles trapezoid, to find the perimeter.
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Perimeter of Trapezoid Calculator
Our Perimeter of Trapezoid Calculator adds up the four sides of a trapezoid. Know all four sides? It adds them and checks they can form a trapezoid. Only know the two bases and the height of an isosceles trapezoid? It finds the slanted legs with Pythagoras first. It also shows the working, a drawing to scale, the area and the angles.
Quick answer
The perimeter of a trapezoid is a + b + c + d, the two bases plus the two legs: 12 + 6 + 5 + 5 = 28 cm.
- Isosceles, from bases and height: P = a + b + 2√(h² + ((a − b) ÷ 2)²)
- Example: bases 16 and 10 with height 4 give legs of 5 and P = 36
- Right trapezoid: one leg is the height, the other is √(h² + (a − b)²)
- Units: a perimeter is a length (cm, m, ft), never cm²
What Is the Perimeter of a Trapezoid?
A trapezoid (a trapezium in British English) is a four-sided shape with one pair of parallel sides, the bases a and b. The other two sides, c and d, are the legs. The perimeter is the total distance around its edge, so it uses the same unit as the sides.
Perimeter of a Trapezoid Formula
- Measure the two bases. These are the parallel sides, a and b.
- Measure the two legs. These are the slanted sides, c and d.
- Use one unit. Convert first if one side is in m and another in cm.
- Add them. 12 + 6 + 5 + 5 = 28, written as 28 cm, not 28 cm².
For an isosceles trapezoid the legs are equal, so the formula shortens to P = a + b + 2c.
Trapezoid Perimeter Examples
| Sides a, b, c, d | Perimeter |
|---|---|
| 10, 6, 5, 5 cm | 26 cm |
| 8, 4, 3, 3 cm | 18 cm |
| 14, 8, 5, 5 m | 32 m |
| 20, 12, 5, 7 ft | 44 ft |
| 12, 7, 12, 13 in | 44 in |
| 2.5, 1.5, 1, 1.2 m | 6.2 m |
Perimeter From the Bases and Height
If you only know the two bases and the height, the legs are not fixed unless the trapezoid is isosceles. Then each leg overhangs the shorter base by (a − b) ÷ 2, and Pythagoras gives its length.
P = a + b + 2c
c ≈ 5.385165
P = 20 + 2√29 ≈ 30.77
Bases 16 and 10 with a height of 4 work out exactly: each leg is √(16 + 9) = 5, so P = 16 + 10 + 5 + 5 = 36. This is the Isosceles mode of the calculator.
Perimeter of a Right Trapezoid
In a right trapezoid one leg stands at a right angle to both bases, so that leg is the height. The slanted leg covers the whole difference between the bases.
P = a + b + h + d
With all four sides known, use Any (4 sides): the calculator tells you whether the trapezoid is isosceles, right or scalene.
Missing Side From the Perimeter
Subtract the three known sides from the perimeter. For an isosceles trapezoid with both legs unknown, subtract the bases and halve what is left.
leg = (P − a − b) ÷ 2
(40 − 14 − 10) ÷ 2 = 8 cm
Common Mistakes
- Adding the height: the height is only a side in a right trapezoid. Otherwise use the slanted legs.
- Assuming equal legs: the bases and height only fix the legs when the trapezoid is isosceles.
- Sides that cannot close: the legs and the difference of the bases must form a triangle. 10, 2, 3, 3 is not a trapezoid.
- Mixed units: 1 m + 50 cm + 40 cm + 40 cm is 2.3 m, not 131.
- Square units: a perimeter is cm or m, not cm² or m².
Key Terms
- Perimeter
- The distance around the trapezoid, P = a + b + c + d.
- Bases
- The two parallel sides, a and b.
- Legs
- The two sides that join the bases, c and d.
- Height
- The distance between the bases, measured at a right angle.
- Isosceles
- A trapezoid whose two legs are equal.
How to Use the Perimeter of Trapezoid Calculator
- Choose what you know. Pick Isosceles to use the two bases and the height, or Any (4 sides) to use both bases and both legs.
- Enter the values. Type the lengths. Decimals and fractions such as 3/4 work. Choose a unit if you want one (mm, cm, m, km, in, ft, yd or mi).
- Read and copy the result. The perimeter appears as you type, with a drawing to scale, the working, the area and the angles. Press Copy to copy it, or Clear or Esc to start again.
Example: a trapezoid-shaped flower bed has a 14 m back edge, an 8 m front edge and 5 m sides. Pick Any (4 sides), enter 14, 8, 5 and 5 and choose m. The perimeter is 32 m, so you need 32 m of edging.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you find the perimeter of a trapezoid?
Add the lengths of its four sides: P = a + b + c + d, where a and b are the parallel bases and c and d are the legs. Bases 12 cm and 6 cm with legs of 5 cm give 28 cm.
How do you find the perimeter of a trapezoid with the bases and height?
For an isosceles trapezoid, each leg is √(h² + ((a − b) ÷ 2)²), so P = a + b + 2√(h² + ((a − b) ÷ 2)²). Bases 16 and 10 with height 4 give legs of 5 and P = 36. If the legs are not equal, the bases and height are not enough: you need the legs too.
What is the perimeter formula for an isosceles trapezoid?
P = a + b + 2c, because both legs have the same length c. Bases 14 and 8 with legs of 5 give 14 + 8 + 10 = 32.
How do you find the perimeter of a right trapezoid?
One leg is the height h and the other is √(h² + (a − b)²). Bases 12 and 7 with height 12 give a slanted leg of 13, so P = 12 + 7 + 12 + 13 = 44.
How do you find a missing side from the perimeter?
Subtract the three known sides from the perimeter: d = P − a − b − c. For an isosceles trapezoid, each leg is (P − a − b) ÷ 2, so a perimeter of 40 with bases 14 and 10 gives legs of 8.
Can any four lengths make a trapezoid?
No. The two legs and the difference between the bases must be able to form a triangle. Bases 10 and 2 differ by 8, so legs of 3 and 3 are too short to reach.
Is the Perimeter of Trapezoid Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Perimeter of Trapezoid Calculator to find the perimeter of any trapezoid from its four sides, or of an isosceles trapezoid from its bases and height.