The perimeter of a trapezoid is equal to the total distance around the limits of the trapezoid. This means that the perimeter of a trapezoid is obtained by adding the lengths of all the sides. Recall that the trapezoid is a 2D geometric figure and that it is a type of quadrilateral, which has two parallel sides and two non-parallel sides. The perpendicular distance between its parallel sides is called the height.

Here, we will learn about the formula to calculate the perimeter of the trapezoid. Also, we will look at some examples in which we will apply this formula.

## Formula for the perimeter of a trapezoid

The perimeter of a trapezoid is found by adding the lengths of all its sides. Therefore, the formula for the perimeter of a trapezoid is given as:

$latex p=a+b+c+d$ |

where “*a, b, c, d*” represent the lengths of the sides of the trapezoid.

### Perimeter of an isosceles trapezoid

If *a* and *b* represent the lengths of the parallel sides and *c* represents the length of the lateral sides in an isosceles trapezoid, then the perimeter will be:

$latex p=a+b+2c$ |

## Perimeter of a trapezoid – Examples with answers

In the following examples, we use the formula for the perimeter of a trapezoid to get the answer. Each example has its respective solution, but it is recommended that you try to solve the exercises yourself before looking at the answer.

**EXAMPLE 1**

A trapezoid has sides of length 6 cm, 8 cm, 5 cm, and 7 cm. What is its perimeter?

##### Solution

Using $latex a, ~b, ~c, ~d$ to represent the lengths of the sides of the trapezoid, we have:

$latex p=a+b+c+d$

$latex p=6+8+5+7$

$latex p=26$

The perimeter of the trapezoid is 26 cm.

**EXAMPLE 2**

A trapezoid has sides with lengths 12 m, 14 m, 7 m, and 9 m. What is its perimeter?

##### Solution

Again, we can use $latex a, ~b, ~c, ~d$ to represent the lengths of the sides of the trapezoid. Replacing these values in the perimeter formula, we have:

$latex p=a+b+c+d$

$latex p=12+14+7+9$

$latex p=42$

The perimeter of the trapezoid is 42 m.

**EXAMPLE 3**

An isosceles trapezoid has two parallel sides measuring 11 m and 13 m. If the lateral sides of the trapezoid are 9 m, what is its perimeter?

##### Solution

We can use $latex a, ~b$ to represent the lengths of the parallel sides and *c* to represent the length of the lateral sides. Therefore, we have:

$latex p=a+b+2c$

$latex p=11+13+2(9)$

$latex p=24+18$

$latex p=42$

The perimeter of the trapezoid is 42 m.

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**EXAMPLE 4**

If a trapezoid has a perimeter of 86 m and has three sides measuring 21 m, 23 m, and 25 m, what is the length of the fourth side?

##### Solution

In this case, we are looking for the length of one of the sides of the trapezoid. We can represent that side with *d*. Therefore, we plug in the given values and solve for *d*:

$latex p=a+b+c+d$

$latex 86=21+23+25+d$

$latex d=86-21-23-25$

$latex d=17$

The length of the fourth side is 17 m.

**EXAMPLE 5**

If an isosceles trapezoid has a perimeter of 64 cm and the length of its parallel sides are 13 cm and 17 cm, what is the length of one of its lateral sides?

##### Solution

We can represent the length of the lateral sides with *c*. Therefore, we plug in the given values into the formula and solve for *c*:

$latex p=a+b+2c$

$latex 64=13+17+2c$

$latex 64=30+2c$

$latex 34=2c$

$latex c=17$

The length of one of the lateral sides is 17 cm.

## Perimeter of a trapezoid – Practice problems

Put into practice what you have learned about the perimeter of a trapezoid with the following problems. Solve the problems and select your answer. Check the chosen answer to verify that you selected the correct one.

## See also

Interested in learning more about trapezoids? Take a look at these pages:

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