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.

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:

1. All we need to do is add the 4 sides together, just as the formula says:
   P = a + b + c + d
2. P = 6 + 8 + 10 + 12 = 36
3. 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:

1. Since the legs are equal in length, c = d. We can replace c + d in the perimeter formula with 2c.
2. 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
3. The length of each leg side is 2.5 meters.