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# Perimeter of a Trapezoid

## 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, and ad are the side lengths. ### Example Problems

Problem 1:
Find the perimeter of a trapezoid with legs 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.

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.

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