A trapezoid is a quadrilateral, or a polygon with 4 sides, v one pair the parallel sides and one pair of non-parallel sides. Outside of phibìc America, trapezoids may be referred to as trapeziums.

How perform we go around finding the perimeter and also area that a trapezoid? review through because that examples.

You are watching: Formula for finding perimeter of a trapezoid

## Finding the Perimeter of a Trapezoid

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We recognize that polygon ABCD is trapezoidal due to the fact that the top and also bottom basic of the trapezoid are parallel.

To discover the perimeter, or the full length of all the political parties of the trapezoid, we simply add the lengths of every side. In this trapezoid ABCD, we watch that the perimeter that 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 optimal base, AB, is 2.The size of the left side length, AD, is 3.The size of the ideal side length, BC, is 2.The perimeter of this trapezoid over is 2 + 2 + 4.5 + 3 = 11.5.

## Finding the Area the a Trapezoid

To uncover the area the a trapezoid, we’ll usage this formula:

The formula multiples the height of a trapezoid *h* v the amount of the 2 bases *a* and *b*, then divides through 2 because the area that the trapezoid is constantly one fifty percent of the parallelogram developed by flipping the trapezoid ~ above itself. Watch the diagram right here how the orange trapezoid is simply the blue trapezoid flipped on itself:

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To uncover the area that a parallelogram, we additionally need the height. As shown in this diagram, the elevation of the parallel is the very same as the height of the trapezoid (both are equal come 2). The elevation of the base of the parallel is the amount of the top base and also the bottom basic of the trapezoid, i beg your pardon in this situation is 2 + 4.5 = 6.5.

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

Image produced in Desmos

In this diagram, we watch that the elevation of the trapezoid is BC, or 2. The is the same as the appropriate hand side of the trapezoid due to the fact that the side connecting vertices B and C is at a ideal angle, or perpendicular, come both the bases. ABCD is well-known as a ideal trapezoid because it contains a appropriate angle.

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The a and b in the formula was standing for the base and also the elevation of the trapezoid, which we understand to be DC = 4.5 and abdominal = 2.

Putting it every together gives us the area the the trapezoid to be:

## Calculating the Area and also Perimeter the a Trapezoid

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

And, friend know just how to calculate the area the a trapezoid using the trapezoid area formula and the lengths because that the base and also the height.

For extra credit, it need to now be clean why the formula because that the area functions the method it does.