Geometry

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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 *a* → *d* 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.**