A trapezoid is a quadrilateral, or a polygon with four sides, with one pair of parallel sides and one pair of non-parallel sides. Outside of North America, trapezoids may be referred to as trapeziums.

How do we go about finding the perimeter and area of a trapezoid? Read through for examples.

## Finding the Perimeter of a Trapezoid

Image created in Desmos

We know that polygon ABCD is trapezoidal because the top and bottom base of the trapezoid are parallel.

To find the perimeter, or the total length of all the sides of the trapezoid, we simply add the lengths of each side. In this trapezoid ABCD, we see that the perimeter of the trapezoid is the sum of AB, BC, DC, and AD:

- The length of the bottom base, DC, is 4.5.
- The length of the top base, AB, is 2.
- The length of the left side length, AD, is 3.
- The length of the right side length, BC, is 2.

The perimeter of this trapezoid above is 2 + 2 + 4.5 + 3 = 11.5.

## Finding the Area of a Trapezoid

To find the area of a trapezoid, we’ll use this formula:

The formula multiples the height of a trapezoid *h* with the sum of the two bases *a* and *b*, then divides by 2 because the area of the trapezoid is always one half of the parallelogram formed by flipping the trapezoid on itself. See the diagram here how the orange trapezoid is just the blue trapezoid flipped on itself:

Image created in Desmos

To find the area of a parallelogram, we also need the height. As shown in this diagram, the height of the parallelogram is the same as the height of the trapezoid (both are equal to 2). The height of the base of the parallelogram is the sum of the top base and the bottom base of the trapezoid, which in this case is 2 + 4.5 = 6.5.

Let’s practice using the formula for the area of a trapezoid.

Image created in Desmos

In this diagram, we see that the height of the trapezoid is BC, or 2. It is the same as the right hand side of the trapezoid because the side connecting vertices B and C is at a right angle, or perpendicular, to both the bases. ABCD is known as a right trapezoid because it contains a right angle.

The a and b in the formula stand for the base and the height of the trapezoid, which we know to be DC = 4.5 and AB = 2.

Putting it all together gives us the area of the trapezoid to be:

## Calculating the Area and Perimeter of a Trapezoid

You now know how to calculate the perimeter of a trapezoid — add all the sides and bases of the trapezoid.

And, you know how to calculate the area of a trapezoid using the trapezoid area formula and the lengths for the base and the height.

For extra credit, it should now be clear why the formula for the area works the way it does.