## Perimeter of a Trapezoid Lesson

### The Perimeter Formula

**A trapezoid is a quadrilateral with only one pair of parallel sides.**

The formula for perimeter is given as:

**P = a + b + c + d**

Where *P* is the perimeter, *a* and *b* are the base lengths, and *c* and *d* are the leg (side) lengths.

INTRODUCING

### Perimeter of a Trapezoid Example Problems

Let's go through a couple of example problems to reinforce our understanding of the perimeter of a trapezoid.

#### Example Problem 1

Find the perimeter of a trapezoid with leg lengths of 10 and 12, and base lengths of 6 and 8.

Solution:

- All we need to do is add the 4 sides together, just as the formula says:

P = a + b + c + d - P = 6 + 8 + 10 + 12 = 36
**The perimeter of the trapezoid is 36.**

#### Example Problem 2

A trapezoidal floor plan's perimeter is measured to be 12 meters. The bases are measured as 3 and 4 meters, and the leg sides (labeled *c* and *d* in the image above) are equal in length. What is the length of the legs?

Solution:

- Since the legs are equal in length, c = d. We can replace c + d in the perimeter formula with 2c.
- Plugging what we know into the formula, we get:

P = a + b + c + d

12 = 3 + 4 + 2c

5 = 2c

c = 2.5, d = 2.5 **The length of each leg side is 2.5 meters.**